Sequence Database

A database with 2076264 machine generated integer and decimal sequences.

Displaying result 0-99 of total 19566. [0] [1] [2] [3] [4] ... [195]

Sequence txkmuesaztw4g

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 0, 1, -1, 0, 0, -1, 0, -1, 0, -1, 0, -1, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 0, -1, 0, -1, -1, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, -1, 0, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(P(n))
P(n)=partition numbers
μ(n)=Möbius function
n≥0
3 operations
Prime

Sequence it0jhqdeappbm

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(P(n))
P(n)=partition numbers
λ(n)=Liouville's function
n≥0
3 operations
Prime
a(n)=(-1)^Ω(P(n))
P(n)=partition numbers
Ω(n)=number of prime divisors of n
n≥0
6 operations
Prime
a(n)=μ(or(6, Ω(P(n))))
P(n)=partition numbers
Ω(n)=number of prime divisors of n
or(a,b)=bitwise or
μ(n)=Möbius function
n≥0
6 operations
Prime

Sequence krm1o4fu23rpp

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(floor(sqrt(n)))
μ(n)=Möbius function
n≥2
4 operations
Prime

Sequence ydebondwjz52p

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(floor(log2(n)))
μ(n)=Möbius function
n≥2
4 operations
Prime

Sequence p1skl520y3o4o

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(σ(φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
σ(n)=divisor sum of n
λ(n)=Liouville's function
n≥1
4 operations
Prime
a(n)=-λ(p(n)*σ(φ(n)))
p(n)=nth prime
ϕ(n)=number of relative primes (Euler's totient)
σ(n)=divisor sum of n
λ(n)=Liouville's function
n≥1
8 operations
Prime

Sequence jog3swipzfpmi

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(floor(sqrt(n)))
λ(n)=Liouville's function
n≥2
4 operations
Prime
a(n)=or(1, μ(floor(sqrt(n))))
μ(n)=Möbius function
or(a,b)=bitwise or
n≥2
6 operations
Prime
a(n)=λ(φ(n))^τ(n)*a(n-1)
a(0)=1
ϕ(n)=number of relative primes (Euler's totient)
λ(n)=Liouville's function
τ(n)=number of divisors of n
n≥2
8 operations
Prime

Sequence 2lauifrshh1ye

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(floor(log2(n)))
λ(n)=Liouville's function
n≥2
4 operations
Prime
a(n)=μ(catalan(floor(log2(n))))
catalan(n)=the catalan numbers
μ(n)=Möbius function
n≥2
5 operations
Prime
a(n)=or(1, μ(floor(log2(n))))
μ(n)=Möbius function
or(a,b)=bitwise or
n≥2
6 operations
Prime

Sequence q5o2yw32qmg1d

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(round(sqrt(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime

Sequence yzo10wilkbc0b

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 0, 1, 0, -1, -1, -1, 0, 1, -1, -1, 0, -1, 0, 1, -1, -1, 0, -1, 1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(P(φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
P(n)=partition numbers
μ(n)=Möbius function
n≥1
4 operations
Prime

Sequence ntwp1gymd1icd

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(P(φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
P(n)=partition numbers
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence 3hpcoptbpb5jm

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(round(sqrt(n)))
λ(n)=Liouville's function
n≥1
4 operations
Prime
a(n)=or(1, μ(round(sqrt(n))))
μ(n)=Möbius function
or(a,b)=bitwise or
n≥1
6 operations
Prime

Sequence friszl5zqq20

1, 1, -1, -1, -1, -1, -1, -1, 0, -1, -1, 0, 0, -1, 0, 0, -1, 0, -1, -1, -1, -1, -1, 1, 0, -1, -1, -1, -1, 0, -1, 1, -1, -1, -1, -1, 0, -1, 0, 0, -1, -1, -1, -1, -1, -1, -1, 1, 0, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(Ω(∑[n]))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
μ(n)=Möbius function
n≥2
4 operations
Prime

Sequence ndutrh0t3v15k

1, 1, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 0, 0, -1, -1, 0, 0, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(or(1, n))
or(a,b)=bitwise or
μ(n)=Möbius function
n≥0
4 operations
Prime

Sequence me5fmgj0nnige

1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(Ω(∑[n]))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
λ(n)=Liouville's function
n≥2
4 operations
Prime
a(n)=or(1, μ(Ω(∑[n])))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
μ(n)=Möbius function
or(a,b)=bitwise or
n≥2
6 operations
Prime
a(n)=(-1)^Ω(Ω(∑[n]))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
n≥2
7 operations
Prime
a(n)=-λ(p(n)*Ω(∑[n]))
p(n)=nth prime
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
λ(n)=Liouville's function
n≥2
8 operations
Prime

Sequence xz5dloz3ctp2d

1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(or(1, n))
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥0
4 operations
Prime
a(n)=(-1)^Ω(or(1, n))
or(a,b)=bitwise or
Ω(n)=number of prime divisors of n
n≥0
7 operations
Prime
a(n)=or(1, λ(or(n, a(n-1)²)))
a(0)=1
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥0
7 operations
Prime

Sequence 0u4lbk5is2drk

1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(23+n)
λ(n)=Liouville's function
n≥2
4 operations
Prime

Sequence kjmdohky4jvkn

1, 1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(τ(P(n)))
P(n)=partition numbers
τ(n)=number of divisors of n
μ(n)=Möbius function
n≥0
4 operations
Prime

Sequence 1k5typwj1vhvh

1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(37+n)
λ(n)=Liouville's function
n≥2
4 operations
Prime

Sequence qldj2a4xq4dzb

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(τ(P(n)))
P(n)=partition numbers
τ(n)=number of divisors of n
λ(n)=Liouville's function
n≥0
4 operations
Prime

Sequence dltpjbm0pmldd

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(lcm(n, 94))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence zihn2id1vk4db

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(lcm(n, 86))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence yretg1wrgqv0i

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(lcm(n, 82))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence h1tqzjl4uuqcd

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(lcm(n, 74))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence 3h2ojrr5gqli

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(lcm(n, 62))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence owhnv4zjsd2nd

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(lcm(n, 58))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence fi5zkb3ktklkj

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(lcm(n, 46))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence wycukvp2gk5ab

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(lcm(n, 38))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence znobwzsevpflo

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(lcm(n, 34))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence luqgmihxz2cnn

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(lcm(n, 26))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence 1qvqvoqljob5k

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(rad(P(n)))
P(n)=partition numbers
rad(n)=square free kernel of n
μ(n)=Möbius function
n≥0
4 operations
Prime
a(n)=λ(rad(P(n)))
P(n)=partition numbers
rad(n)=square free kernel of n
λ(n)=Liouville's function
n≥0
4 operations
Prime
a(n)=1/λ(rad(P(n)))
P(n)=partition numbers
rad(n)=square free kernel of n
λ(n)=Liouville's function
n≥0
6 operations
Prime
a(n)=or(1, λ(rad(P(n))))
P(n)=partition numbers
rad(n)=square free kernel of n
λ(n)=Liouville's function
or(a,b)=bitwise or
n≥0
6 operations
Prime

Sequence qrpvgo5gtojud

1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(lcm(n, 22))
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence 12sbyzb2uwgi

1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(or(24, n))
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥1
4 operations
Prime

Sequence s3r2iqyw2fyno

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -3, -1, -1, -1, -1, -1, -3, -3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -3, -3, -3, -3, -1, -1, -1, -1, -1, 1, 1, -1, -1, -3, -3, -3, -1, -3, -3, -3, -3, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=or(1, ∑[μ(n)])
μ(n)=Möbius function
∑(a)=partial sums of a
or(a,b)=bitwise or
n≥1
5 operations
Prime

Sequence d20rbxayewhhk

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(P(floor(sqrt(n))))
P(n)=partition numbers
λ(n)=Liouville's function
n≥2
5 operations
Prime
a(n)=μ(P(floor(sqrt(n))))
P(n)=partition numbers
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence ydmrnom12m4oo

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(P(Ω(∑[n])))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
P(n)=partition numbers
λ(n)=Liouville's function
n≥2
5 operations
Prime
a(n)=μ(P(Ω(∑[n])))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
P(n)=partition numbers
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence j3gulp5451f1f

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(P(round(sqrt(n))))
P(n)=partition numbers
μ(n)=Möbius function
n≥1
5 operations
Prime
a(n)=λ(P(round(sqrt(n))))
P(n)=partition numbers
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence behcj4oh0gl5h

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(round(root(3, n)))
root(n,a)=the n-th root of a
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence ik5m02k4w1hac

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(round(root(3, n)))
root(n,a)=the n-th root of a
λ(n)=Liouville's function
n≥2
5 operations
Prime
a(n)=μ(catalan(round(root(3, n))))
root(n,a)=the n-th root of a
catalan(n)=the catalan numbers
μ(n)=Möbius function
n≥2
6 operations
Prime

Sequence u4hllegykbpsc

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(round(n^Pólya_D3))
Pólya_D3=0.3405... (Pólya random walk 3D)
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence bwx5nkgktuezc

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(round(n^Pólya_D3))
Pólya_D3=0.3405... (Pólya random walk 3D)
λ(n)=Liouville's function
n≥2
5 operations
Prime

Sequence b5au4judd2elp

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(floor(log(composite(n))))
composite(n)=nth composite number
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence yezjy55zsprpb

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(P(ceil(sqrt(n))))
P(n)=partition numbers
μ(n)=Möbius function
n≥0
5 operations
Prime
a(n)=λ(P(ceil(sqrt(n))))
P(n)=partition numbers
λ(n)=Liouville's function
n≥0
5 operations
Prime

Sequence rhqhn5hcf5u3n

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(τ(floor(sqrt(n))))
τ(n)=number of divisors of n
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence t5ucizmnqaylh

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(τ(floor(sqrt(n))))
τ(n)=number of divisors of n
λ(n)=Liouville's function
n≥2
5 operations
Prime
a(n)=μ(rad(floor(sqrt(n))))
rad(n)=square free kernel of n
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence kpcmkgnkwdt1p

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(τ(round(sqrt(n))))
τ(n)=number of divisors of n
μ(n)=Möbius function
n≥1
5 operations
Prime

Sequence z3fv3ob1pkbgn

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(agc(or(35, n)))
or(a,b)=bitwise or
agc(n)=number of factorizations into prime powers (abelian group count)
λ(n)=Liouville's function
n≥2
5 operations
Prime

Sequence py2tlq33ryhvb

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(τ(round(sqrt(n))))
τ(n)=number of divisors of n
λ(n)=Liouville's function
n≥1
5 operations
Prime
a(n)=μ(rad(round(sqrt(n))))
rad(n)=square free kernel of n
μ(n)=Möbius function
n≥1
5 operations
Prime

Sequence yow2gj2jnyu2k

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(round(root(e, n)))
e=2.7182... (Euler e)
root(n,a)=the n-th root of a
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence 5edbnx045ew3c

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(round(root(e, n)))
e=2.7182... (Euler e)
root(n,a)=the n-th root of a
λ(n)=Liouville's function
n≥2
5 operations
Prime
a(n)=μ(catalan(round(root(e, n))))
e=2.7182... (Euler e)
root(n,a)=the n-th root of a
catalan(n)=the catalan numbers
μ(n)=Möbius function
n≥2
6 operations
Prime

Sequence 2yinvj2zmonhe

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(round(n^Artins))
Artins=0.3739... (Artins)
μ(n)=Möbius function
n≥1
5 operations
Prime

Sequence 5nqdyu1bbepjf

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(round(n^Artins))
Artins=0.3739... (Artins)
λ(n)=Liouville's function
n≥1
5 operations
Prime
a(n)=μ(catalan(ceil(root(3, n))))
root(n,a)=the n-th root of a
catalan(n)=the catalan numbers
μ(n)=Möbius function
n≥0
6 operations
Prime

Sequence afbn5520liryg

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(τ(Ω(∑[n])))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
τ(n)=number of divisors of n
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence lgyth4xlu5b5l

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(τ(Ω(∑[n])))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
τ(n)=number of divisors of n
λ(n)=Liouville's function
n≥2
5 operations
Prime
a(n)=μ(rad(Ω(∑[n])))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
μ(n)=Möbius function
n≥2
5 operations
Prime
a(n)=(-1)^ω(Ω(∑[n]))
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
ω(n)=number of distinct prime divisors of n
n≥2
7 operations
Prime

Sequence hrqcrtyrkb5pg

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(ω(composite(∑[n])))
∑(a)=partial sums of a
composite(n)=nth composite number
ω(n)=number of distinct prime divisors of n
μ(n)=Möbius function
n≥2
5 operations
Prime
a(n)=λ(ω(composite(∑[n])))
∑(a)=partial sums of a
composite(n)=nth composite number
ω(n)=number of distinct prime divisors of n
λ(n)=Liouville's function
n≥2
5 operations
Prime

Sequence y22mbasd2ilhd

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(catalan(ceil(log(n))))
catalan(n)=the catalan numbers
μ(n)=Möbius function
n≥1
5 operations
Prime
a(n)=λ(catalan(ceil(log(n))))
catalan(n)=the catalan numbers
λ(n)=Liouville's function
n≥1
5 operations
Prime
a(n)=1-and(2, ceil(log(n)))
and(a,b)=bitwise and
n≥1
7 operations
Power

Sequence tmh3siqpy4yhk

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(catalan(ω(∑[n])))
∑(a)=partial sums of a
ω(n)=number of distinct prime divisors of n
catalan(n)=the catalan numbers
μ(n)=Möbius function
n≥1
5 operations
Prime
a(n)=λ(catalan(ω(∑[n])))
∑(a)=partial sums of a
ω(n)=number of distinct prime divisors of n
catalan(n)=the catalan numbers
λ(n)=Liouville's function
n≥1
5 operations
Prime
a(n)=1-and(2, ω(∑[n]))
∑(a)=partial sums of a
ω(n)=number of distinct prime divisors of n
and(a,b)=bitwise and
n≥1
7 operations
Prime

Sequence cmkwhq0ohu0wi

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(xor(97, φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
xor(a,b)=bitwise exclusive or
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence p0rlbbznanc3k

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(or(76, φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence wfdmyboqdhmql

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(round(log(σ(n))))
σ(n)=divisor sum of n
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence a2ywcovsmai1n

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(95+φ(n))
ϕ(n)=number of relative primes (Euler's totient)
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence rf40qwwsoyd2g

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(or(68, φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence v23l3gmhqfqxg

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(round(log(σ(n))))
σ(n)=divisor sum of n
λ(n)=Liouville's function
n≥2
5 operations
Prime
a(n)=μ(catalan(round(log(σ(n)))))
σ(n)=divisor sum of n
catalan(n)=the catalan numbers
μ(n)=Möbius function
n≥2
6 operations
Prime

Sequence 1stkqgabzoyoo

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, 0, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(Ω(lcm(n, 2)))
lcm(a,b)=least common multiple
Ω(n)=number of prime divisors of n
μ(n)=Möbius function
n≥1
5 operations
Prime

Sequence kghmucuyatmxe

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(Ω(lcm(n, 2)))
lcm(a,b)=least common multiple
Ω(n)=number of prime divisors of n
λ(n)=Liouville's function
n≥1
5 operations
Prime
a(n)=μ(catalan(Ω(lcm(n, 2))))
lcm(a,b)=least common multiple
Ω(n)=number of prime divisors of n
catalan(n)=the catalan numbers
μ(n)=Möbius function
n≥1
6 operations
Prime

Sequence vsgucgefb5wle

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(Ω(and(62, n)))
and(a,b)=bitwise and
Ω(n)=number of prime divisors of n
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence vaulbim12czoi

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, 0, 0, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(τ(or(1, n)))
or(a,b)=bitwise or
τ(n)=number of divisors of n
μ(n)=Möbius function
n≥0
5 operations
Prime

Sequence zlaqkazchcbxh

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, -1, 0, -1, -1, -1, 0, 1, -1, -1, -1, -1, 0, -1, -1, 1, -1, 0, -1, -1, -1, 0, -1, -1, -1, -1, 1, 0, -1, -1, -1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(or(1, φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
or(a,b)=bitwise or
μ(n)=Möbius function
n≥1
5 operations
Prime

Sequence sznkdobmh14zm

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(Ω(and(62, n)))
and(a,b)=bitwise and
Ω(n)=number of prime divisors of n
λ(n)=Liouville's function
n≥2
5 operations
Prime

Sequence usw5sg5tm3ek

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(rad(or(1, n)))
or(a,b)=bitwise or
rad(n)=square free kernel of n
μ(n)=Möbius function
n≥0
5 operations
Prime
a(n)=λ(rad(or(1, n)))
or(a,b)=bitwise or
rad(n)=square free kernel of n
λ(n)=Liouville's function
n≥0
5 operations
Prime
a(n)=(-1)^ω(or(1, n))
or(a,b)=bitwise or
ω(n)=number of distinct prime divisors of n
n≥0
7 operations
Prime
a(n)=or(1, -and(1, ω(or(1, n))))
or(a,b)=bitwise or
ω(n)=number of distinct prime divisors of n
and(a,b)=bitwise and
n≥0
9 operations
Prime

Sequence t2ehstvw5zdof

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(τ(or(1, n)))
or(a,b)=bitwise or
τ(n)=number of divisors of n
λ(n)=Liouville's function
n≥0
5 operations
Prime

Sequence 0qgluocqpmrqi

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(or(1, φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥1
5 operations
Prime
a(n)=-λ(lcm(1+φ(n), 2))
ϕ(n)=number of relative primes (Euler's totient)
lcm(a,b)=least common multiple
λ(n)=Liouville's function
n≥1
8 operations
Prime

Sequence ggtmbqgh0ju0e

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(82-φ(n))
ϕ(n)=number of relative primes (Euler's totient)
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence piw5u2ywybjtl

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(or(25, φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥1
5 operations
Prime
a(n)=μ(P(and(6, φ(n))))
ϕ(n)=number of relative primes (Euler's totient)
and(a,b)=bitwise and
P(n)=partition numbers
μ(n)=Möbius function
n≥1
6 operations
Prime

Sequence yquuqckwua1lg

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=-λ(or(83, n))
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥2
5 operations
Prime
a(n)=-μ(or(83, n))
or(a,b)=bitwise or
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence aosvtkuhjmcy

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(σ(or(83, n)))
or(a,b)=bitwise or
σ(n)=divisor sum of n
λ(n)=Liouville's function
n≥2
5 operations
Prime

Sequence ec1zyuuaqznvp

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(catalan(floor(sqrt(n))))
catalan(n)=the catalan numbers
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence 4wgizf3p0ye4h

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(xor(25, φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
xor(a,b)=bitwise exclusive or
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence coma5di23fcdk

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(99+φ(n))
ϕ(n)=number of relative primes (Euler's totient)
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence hxz1o5lrx05tc

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(57+φ(n))
ϕ(n)=number of relative primes (Euler's totient)
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence bzf31ticrl2uf

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(47-φ(n))
ϕ(n)=number of relative primes (Euler's totient)
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence figpwaeptzpgb

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(xor(47, φ(n)))
ϕ(n)=number of relative primes (Euler's totient)
xor(a,b)=bitwise exclusive or
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence h4em2o1ac01

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(rad(or(97, n)))
or(a,b)=bitwise or
rad(n)=square free kernel of n
λ(n)=Liouville's function
n≥2
5 operations
Prime
a(n)=μ(rad(or(97, n)))
or(a,b)=bitwise or
rad(n)=square free kernel of n
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence dybrimqnn04sk

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(τ(or(97, n)))
or(a,b)=bitwise or
τ(n)=number of divisors of n
λ(n)=Liouville's function
n≥2
5 operations
Prime

Sequence uscacsqvr1tqc

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(Δ[p(n)²])
p(n)=nth prime
Δ(a)=differences of a
λ(n)=Liouville's function
n≥2
5 operations
Prime

Sequence fam2kkpa0yyhj

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(catalan(round(sqrt(n))))
catalan(n)=the catalan numbers
μ(n)=Möbius function
n≥1
5 operations
Prime

Sequence qjc1ssxosnggd

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(floor(log2(zetazero(n))))
zetazero(n)=non trivial zeros of Riemann zeta
λ(n)=Liouville's function
n≥2
5 operations
Prime
a(n)=μ(Ω(ceil(log2(zetazero(n)))))
zetazero(n)=non trivial zeros of Riemann zeta
Ω(n)=number of prime divisors of n
μ(n)=Möbius function
n≥2
6 operations
Prime

Sequence vto4fj0xzztoh

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(floor(root(Tribonacci, n)))
Tribonacci=1.8392... (Tribonacci)
root(n,a)=the n-th root of a
μ(n)=Möbius function
n≥2
5 operations
Prime

Sequence r1t4uqignqptk

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(round(log(p(n))))
p(n)=nth prime
μ(n)=Möbius function
n≥1
5 operations
Prime

Sequence rb3z0jyyd3hj

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(∑[or(38, n)])
or(a,b)=bitwise or
∑(a)=partial sums of a
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence h41k3yfl3wdnp

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(xor(36, ∑[n]))
∑(a)=partial sums of a
xor(a,b)=bitwise exclusive or
λ(n)=Liouville's function
n≥2
5 operations
Prime

Sequence cugeefsczllxe

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(35+σ(n))
σ(n)=divisor sum of n
λ(n)=Liouville's function
n≥2
5 operations
Prime

Sequence cftmpk3oafhan

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(or(57, P(n)))
P(n)=partition numbers
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥0
5 operations
Prime

Sequence o5djgftur0nym

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=∏[λ(xor(93, n))]
xor(a,b)=bitwise exclusive or
λ(n)=Liouville's function
∏(a)=partial products of a
n≥2
5 operations
Prime

Sequence hyno5d2oym5pk

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(∑[6+a(n-1)])
a(0)=4
∑(a)=partial sums of a
λ(n)=Liouville's function
n≥0
5 operations
Prime

Sequence ydk1dgpeb1ogl

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(or(57, ∑[n]))
∑(a)=partial sums of a
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥0
5 operations
Prime

Sequence ercrxk1dwrwjd

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(or(25, P(n)))
P(n)=partition numbers
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥0
5 operations
Prime

Sequence ikczrrixre4el

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(or(25, ∑[n]))
∑(a)=partial sums of a
or(a,b)=bitwise or
λ(n)=Liouville's function
n≥0
5 operations
Prime

Sequence c4jjz440djxnp

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(floor(root(Tribonacci, n)))
Tribonacci=1.8392... (Tribonacci)
root(n,a)=the n-th root of a
λ(n)=Liouville's function
n≥2
5 operations
Prime

Sequence yyedm03k0edjj

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=μ(catalan(round(log2(n))))
catalan(n)=the catalan numbers
μ(n)=Möbius function
n≥1
5 operations
Prime

Sequence ig2ybs1jp4mxd

1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, more...

integer, non-monotonic, +-, A071759 (weak, multiple)

a(n)=λ(catalan(round(log2(n))))
catalan(n)=the catalan numbers
λ(n)=Liouville's function
n≥1
5 operations
Prime

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