Sequence Database

A database with 2076264 machine generated integer and decimal sequences.

Displaying result 1367800-1367899 of total 1462982. [0] ... [13674] [13675] [13676] [13677] [13678] [13679] [13680] [13681] [13682] ... [14629]

Sequence r2eeeonp4hhci

1, 2, 4, 8, 8, 8, 8, 48, more...

integer, monotonic, +

a(n)=τ(Δ[φ(p(a(n-1)))])
a(0)=3
p(n)=nth prime
ϕ(n)=number of relative primes (Euler's totient)
Δ(a)=differences of a
τ(n)=number of divisors of n
n≥0
5 operations
Prime

Sequence dvg3nvwc3xzpp

1, 2, 4, 8, 12, 12, 8, 32, more...

integer, non-monotonic, +

a(n)=τ(Δ[p(σ(a(n-1)))])
a(0)=1
σ(n)=divisor sum of n
p(n)=nth prime
Δ(a)=differences of a
τ(n)=number of divisors of n
n≥0
5 operations
Prime

Sequence b4r3capy3ioli

1, 2, 4, 8, 12, 12, 20, 24, 16, 32, 36, 24, 44, 40, 36, 56, 60, 40, 48, 72, 48, 80, 84, 48, 92, 84, 64, 104, 80, 72, 116, 120, 72, 96, 132, 88, 140, 144, 80, 120, 156, 108, 164, 128, 112, 176, 144, 120, 144, 192, more...

integer, non-monotonic, +

a(n)=φ(∑[composite(τ(a(n-1)))])
a(0)=2
τ(n)=number of divisors of n
composite(n)=nth composite number
∑(a)=partial sums of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence tcyfxrfvbmz2m

1, 2, 4, 8, 18, 24, 32, 48, 72, 128, 216, 508, 288, 448, 576, 1312, 720, 1484, 704, 1024, 1376, 2000, 2688, 4224, 3840, 4992, 2944, 12096, 3072, 4320, 8640, 8832, 17280, 13824, 14080, 30560, 10368, 44544, 20736, 33792, 27984, more...

integer, non-monotonic, +

a(n)=φ(φ(∑[composite(a(n-1))]))
a(0)=4
composite(n)=nth composite number
∑(a)=partial sums of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence xemzlwixf2ntn

1, 2, 4, 8, 32, 130, 684, 3648, 47352, more...

integer, strictly-monotonic, +

a(n)=φ(∑[σ(p(a(n-1)))])
a(0)=1
p(n)=nth prime
σ(n)=divisor sum of n
∑(a)=partial sums of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence 05tj5m5rs34r

1, 2, 4, 8, 36, 232, 2144, 12000, more...

integer, strictly-monotonic, +

a(n)=φ(composite(Δ[p(a(n-1))]))
a(0)=2
p(n)=nth prime
Δ(a)=differences of a
composite(n)=nth composite number
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence he0jhf2hmqghe

1, 2, 4, 8, 40, 432, 4048, 28512, more...

integer, strictly-monotonic, +

a(n)=φ(Δ[σ(p(a(n-1)))])
a(0)=1
p(n)=nth prime
σ(n)=divisor sum of n
Δ(a)=differences of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence 5hcsmja41wqak

1, 2, 4, 12, 32, 256, 718, 8112, 36832, more...

integer, strictly-monotonic, +

a(n)=φ(∑[p(σ(a(n-1)))])
a(0)=1
σ(n)=divisor sum of n
p(n)=nth prime
∑(a)=partial sums of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence z3szzvwtnvvc

1, 2, 4, 12, 72, 336, 4536, 28296, more...

integer, strictly-monotonic, +

a(n)=φ(σ(Δ[p(a(n-1))]))
a(0)=2
p(n)=nth prime
Δ(a)=differences of a
σ(n)=divisor sum of n
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence 2tgnx0xou4msc

1, 2, 4, 20, 160, 3456, more...

integer, strictly-monotonic, +

a(n)=φ(composite(∏[p(a(n-1))]))
a(0)=1
p(n)=nth prime
∏(a)=partial products of a
composite(n)=nth composite number
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence t3i03v35eek2n

1, 2, 4, 24, 96, 672, 7992, more...

integer, strictly-monotonic, +

a(n)=φ(Δ[σ(p(a(n-1)))])
a(0)=2
p(n)=nth prime
σ(n)=divisor sum of n
Δ(a)=differences of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence earxvvk5ys2so

1, 2, 4, 24, 288, 9216, more...

integer, strictly-monotonic, +

a(n)=φ(σ(∏[p(a(n-1))]))
a(0)=1
p(n)=nth prime
∏(a)=partial products of a
σ(n)=divisor sum of n
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence oz5biivs3iszn

1, 2, 4, 36, 160, 2240, 22528, more...

integer, strictly-monotonic, +

a(n)=φ(φ(Δ[p(a(n-1))]))
a(0)=4
p(n)=nth prime
Δ(a)=differences of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence 5khfif3pitoim

1, 2, 4, 46, 120, 2184, 11512, more...

integer, strictly-monotonic, +

a(n)=φ(∑[p(composite(a(n-1)))])
a(0)=1
composite(n)=nth composite number
p(n)=nth prime
∑(a)=partial sums of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence n3umk5zaltjrn

1, 2, 5, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 3, 1, 1, 1, 2, 6, 2, 1, 1, 1, 1, 1, 7, 4, 1, 1, 1, 1, 2, 2, 2, 15, 1, 3, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, more...

integer, non-monotonic, +

a(n)=agc(∑[σ(gpf(a(n-1)))])
a(0)=5
gpf(n)=greatest prime factor of n
σ(n)=divisor sum of n
∑(a)=partial sums of a
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence olbhaoeobqehe

1, 2, 5, 1, 6, 2, 1, 3, more...

integer, non-monotonic, +

a(n)=agc(∑[σ(composite(a(n-1)))])
a(0)=4
composite(n)=nth composite number
σ(n)=divisor sum of n
∑(a)=partial sums of a
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence y3ihqudmluwgf

1, 2, 5, 2, 3, 2, 2, 7, 5, 2, 2, 2, more...

integer, non-monotonic, +

a(n)=lpf(composite(Δ[σ(a(n-1))]))
a(0)=5
σ(n)=divisor sum of n
Δ(a)=differences of a
composite(n)=nth composite number
lpf(n)=least prime factor of n
n≥0
5 operations
Prime

Sequence irh1ikmyltgjc

1, 2, 5, 2, 3, 2, 7, 4, 3, 2, 5, 2, 3, 2, 11, 2, 6, 2, 5, 2, 3, 2, 7, 4, 3, 6, 5, 2, 3, 2, 15, 2, 3, 2, 10, 2, 3, 2, 7, 2, 3, 2, 5, 4, 3, 2, 11, 4, 6, 2, more...

integer, non-monotonic, +

a(n)=agc(∑[φ(composite(a(n-1)))])
a(0)=5
composite(n)=nth composite number
ϕ(n)=number of relative primes (Euler's totient)
∑(a)=partial sums of a
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence j1mi3roidcffn

1, 2, 5, 2, 7, 2, 2, 2, 2, 2, 2, 2, more...

integer, non-monotonic, +

a(n)=lpf(τ(Δ[σ(a(n-1))]))
a(0)=5
σ(n)=divisor sum of n
Δ(a)=differences of a
τ(n)=number of divisors of n
lpf(n)=least prime factor of n
n≥0
5 operations
Prime

Sequence s21hjk13tta4n

1, 2, 5, 3, 7, 5, 5, 5, 3, 2, 3, 3, more...

integer, non-monotonic, +

a(n)=gpf(τ(Δ[σ(a(n-1))]))
a(0)=5
σ(n)=divisor sum of n
Δ(a)=differences of a
τ(n)=number of divisors of n
gpf(n)=greatest prime factor of n
n≥0
5 operations
Prime

Sequence 200q4b30wij1g

1, 2, 5, 3, 17, 131, 19, 229, 3947, more...

integer, non-monotonic, +

a(n)=gpf(∑[σ(p(a(n-1)))])
a(0)=1
p(n)=nth prime
σ(n)=divisor sum of n
∑(a)=partial sums of a
gpf(n)=greatest prime factor of n
n≥0
5 operations
Prime

Sequence covrugb2s5j1g

1, 2, 5, 5, 3, 2, 3, 2, 3, 2, 2, 6, 6, 3, 1, 2, 4, 1, 6, 1, 3, 3, 3, 5, more...

integer, non-monotonic, +

a(n)=Ω(∑[composite(composite(a(n-1)))])
a(0)=2
composite(n)=nth composite number
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
n≥0
5 operations
Prime

Sequence uyo0vptmuyq4f

1, 2, 5, 5, 7, 59, 269, 251, more...

integer, non-monotonic, +

a(n)=gpf(composite(Δ[p(a(n-1))]))
a(0)=2
p(n)=nth prime
Δ(a)=differences of a
composite(n)=nth composite number
gpf(n)=greatest prime factor of n
n≥0
5 operations
Prime

Sequence wp4wroiaxn0xp

1, 2, 5, 6, 7, 10, 10, 10, 6, 2, 6, 6, more...

integer, non-monotonic, +

a(n)=rad(τ(Δ[σ(a(n-1))]))
a(0)=5
σ(n)=divisor sum of n
Δ(a)=differences of a
τ(n)=number of divisors of n
rad(n)=square free kernel of n
n≥0
5 operations
Prime

Sequence fd231wqj3se1j

1, 2, 5, 11, 41, 19, more...

integer, non-monotonic, +

a(n)=gpf(composite(∏[p(a(n-1))]))
a(0)=1
p(n)=nth prime
∏(a)=partial products of a
composite(n)=nth composite number
gpf(n)=greatest prime factor of n
n≥0
5 operations
Prime

Sequence pxz3ccklyegkn

1, 2, 5, 71, 263, more...

integer, strictly-monotonic, +

a(n)=gpf(∑[p(p(a(n-1)))])
a(0)=1
p(n)=nth prime
∑(a)=partial sums of a
gpf(n)=greatest prime factor of n
n≥0
5 operations
Prime

Sequence czfxgsr4l31pf

1, 2, 6, 2, 2, 6, 6, 10, 6, 2, 190, 786, 1326, 51502, 3162, more...

integer, non-monotonic, +

a(n)=rad(φ(∑[σ(a(n-1))]))
a(0)=2
σ(n)=divisor sum of n
∑(a)=partial sums of a
ϕ(n)=number of relative primes (Euler's totient)
rad(n)=square free kernel of n
n≥0
5 operations
Prime

Sequence dazs235zwm0yo

1, 2, 6, 6, 4, 82, 130, 196, 40, 36, 562, 16, 1020, 78, 82, 2236, 946, 12, 4462, 78, 178, 4156, 420, 12210, 14682, 17572, 996, 22, 102, 1570, 136, 15808, 11058, 64278, 420, 172, 1482, 1428, 2082, 60, 96, 70, more...

integer, non-monotonic, +

a(n)=φ(gpf(∑[composite(a(n-1))]))
a(0)=2
composite(n)=nth composite number
∑(a)=partial sums of a
gpf(n)=greatest prime factor of n
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence xyieaggx5h4gb

1, 2, 6, 6, 4, 82, 130, 196, 240, 360, 562, 128, 1020, 1248, 984, 2236, 1892, 480, 4462, 1872, 3204, 4156, 840, 12210, 14682, 17572, 11952, 176, 14688, 15700, 4896, 31616, 44232, 64278, 48720, 28208, 97812, 5712, 24984, 3600, 126720, 12320, more...

integer, non-monotonic, +

a(n)=φ(rad(∑[composite(a(n-1))]))
a(0)=2
composite(n)=nth composite number
∑(a)=partial sums of a
rad(n)=square free kernel of n
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence hy2vnxy540dyd

1, 2, 6, 6, 6, 6, 546, 2, 30, 12810, more...

integer, non-monotonic, +

a(n)=rad(σ(∑[p(a(n-1))]))
a(0)=1
p(n)=nth prime
∑(a)=partial sums of a
σ(n)=divisor sum of n
rad(n)=square free kernel of n
n≥0
5 operations
Prime

Sequence 0kadfezobanom

1, 2, 6, 6, 10, 82, 130, 14, 30, 30, 562, 6, 510, 78, 246, 1118, 946, 30, 4462, 78, 534, 2078, 210, 12210, 14682, 8786, 498, 66, 102, 1570, 102, 494, 11058, 21426, 6090, 3526, 16302, 714, 2082, 30, 330, 770, more...

integer, non-monotonic, +

a(n)=rad(φ(∑[composite(a(n-1))]))
a(0)=2
composite(n)=nth composite number
∑(a)=partial sums of a
ϕ(n)=number of relative primes (Euler's totient)
rad(n)=square free kernel of n
n≥0
5 operations
Prime

Sequence gy1oszoywzfhl

1, 2, 6, 6, 114, 178, 5826, 12090, more...

integer, monotonic, +

a(n)=rad(Δ[φ(p(a(n-1)))])
a(0)=3
p(n)=nth prime
ϕ(n)=number of relative primes (Euler's totient)
Δ(a)=differences of a
rad(n)=square free kernel of n
n≥0
5 operations
Prime

Sequence 1nkwl1dkahthd

1, 2, 6, 8, 8, 16, 24, 48, 120, 96, 144, 192, 192, 360, 128, 440, 324, 480, 576, 576, 384, 2048, 3248, 3096, 1920, 5184, 2592, 4608, 6144, 3072, 6336, 11648, 9216, 23200, 21384, 14480, 8832, 37296, 27216, 13440, 46656, 41472, more...

integer, non-monotonic, +

a(n)=φ(φ(∑[composite(a(n-1))]))
a(0)=3
composite(n)=nth composite number
∑(a)=partial sums of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence ogl0eedwth1ze

1, 2, 6, 8, 18, 24, 8, 30, more...

integer, non-monotonic, +

a(n)=τ(σ(Δ[p(a(n-1))]))
a(0)=2
p(n)=nth prime
Δ(a)=differences of a
σ(n)=divisor sum of n
τ(n)=number of divisors of n
n≥0
5 operations
Prime

Sequence omv35biidxnag

1, 2, 6, 8, 56, 192, 1344, 9504, more...

integer, strictly-monotonic, +

a(n)=φ(φ(∑[p(a(n-1))]))
a(0)=3
p(n)=nth prime
∑(a)=partial sums of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence hlunyjxbsej0i

1, 2, 6, 12, 24, 44, more...

integer, strictly-monotonic, +

a(n)=τ(σ(∏[p(a(n-1))]))
a(0)=1
p(n)=nth prime
∏(a)=partial products of a
σ(n)=divisor sum of n
τ(n)=number of divisors of n
n≥0
5 operations
Prime

Sequence zpsexb2gg1p2l

1, 2, 6, 14, 22, 114, 326, 706, 638, 393, 813, 178, 451, 902, 310, 170, 435, 879, 217, 130, 358, 758, 1351, 2139, 3103, 78, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, more...

integer, non-monotonic, +

a(n)=rad(composite(floor(zetazero(a(n-1)))))
a(0)=1
zetazero(n)=non trivial zeros of Riemann zeta
composite(n)=nth composite number
rad(n)=square free kernel of n
n≥0
5 operations
Prime

Sequence 53tnhch3hh3jm

1, 2, 6, 16, 52, 232, 1088, 6144, more...

integer, strictly-monotonic, +

a(n)=φ(∑[σ(p(a(n-1)))])
a(0)=2
p(n)=nth prime
σ(n)=divisor sum of n
∑(a)=partial sums of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence z3z0l2lc55k2g

1, 2, 6, 18, 102, 858, 5600, 39040, more...

integer, strictly-monotonic, +

a(n)=φ(∑[σ(σ(a(n-1)))])
a(0)=2
σ(n)=divisor sum of n
∑(a)=partial sums of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence qeovjuehgmosj

1, 2, 6, 30, 210, 1470, 10290, 72030, 504210, 3529470, 24706290, 172944030, 1210608210, 8474257470, 59319802290, 415238616030, 2906670312210, 20346692185470, 142426845298290, 996987917088030, more...

integer, strictly-monotonic, +

a(n)=∏[p(τ(σ(a(n-1))))]
a(0)=1
σ(n)=divisor sum of n
τ(n)=number of divisors of n
p(n)=nth prime
∏(a)=partial products of a
n≥0
5 operations
Prime

Sequence 23kijbxevcs4o

1, 2, 6, 42, 2226, 3363486, 456515864322, more...

integer, strictly-monotonic, +

a(n)=∏[p(φ(p(a(n-1))))]
a(0)=1
p(n)=nth prime
ϕ(n)=number of relative primes (Euler's totient)
∏(a)=partial products of a
n≥0
5 operations
Prime

Sequence pttpd5o2cwguf

1, 2, 6, 57, 205, 10, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, 74, 35, more...

integer, non-monotonic, +

a(n)=rad(composite(round(zetazero(a(n-1)))))
a(0)=1
zetazero(n)=non trivial zeros of Riemann zeta
composite(n)=nth composite number
rad(n)=square free kernel of n
n≥0
5 operations
Prime

Sequence mgvtgspbseuyf

1, 2, 6, 72, 2880, more...

integer, strictly-monotonic, +

a(n)=φ(∏[σ(p(a(n-1)))])
a(0)=1
p(n)=nth prime
σ(n)=divisor sum of n
∏(a)=partial products of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence vdmqhcn02e2kg

1, 2, 6, 78, 5694, 244842, 27667146, 2019701658, 86847171294, 9813730356222, 716402316004206, more...

integer, strictly-monotonic, +

a(n)=∏[p(rad(composite(a(n-1))))]
a(0)=1
composite(n)=nth composite number
rad(n)=square free kernel of n
p(n)=nth prime
∏(a)=partial products of a
n≥0
5 operations
Prime

Sequence idhh0qlkav2rd

1, 2, 8, 4, 4, 32, more...

integer, non-monotonic, +

a(n)=τ(Δ[p(composite(a(n-1)))])
a(0)=1
composite(n)=nth composite number
p(n)=nth prime
Δ(a)=differences of a
τ(n)=number of divisors of n
n≥0
5 operations
Prime

Sequence fgq15javdz5gj

1, 2, 8, 36, 352, 1940, 14400, more...

integer, strictly-monotonic, +

a(n)=φ(Δ[φ(p(a(n-1)))])
a(0)=4
p(n)=nth prime
ϕ(n)=number of relative primes (Euler's totient)
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence wagazrjm35tuk

1, 2, 8, 48, 384, 7116, 18720, more...

integer, strictly-monotonic, +

a(n)=φ(Δ[σ(σ(a(n-1)))])
a(0)=2
σ(n)=divisor sum of n
Δ(a)=differences of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence 1zrazv2id53af

1, 2, 8, 70, 3144, more...

integer, strictly-monotonic, +

a(n)=φ(∑[p(p(a(n-1)))])
a(0)=1
p(n)=nth prime
∑(a)=partial sums of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence 0h42h3rat4g3g

1, 2, 8, 128, 30720, 388485120, more...

integer, strictly-monotonic, +

a(n)=∏[φ(p(p(a(n-1))))]
a(0)=1
p(n)=nth prime
ϕ(n)=number of relative primes (Euler's totient)
∏(a)=partial products of a
n≥0
5 operations
Prime

Sequence oor5o3rnnt3gb

1, 2, 10, 6, 34, 262, 38, 1374, 55258, more...

integer, non-monotonic, +

a(n)=rad(∑[σ(p(a(n-1)))])
a(0)=1
p(n)=nth prime
σ(n)=divisor sum of n
∑(a)=partial sums of a
rad(n)=square free kernel of n
n≥0
5 operations
Prime

Sequence aoqlucfvgrn3l

1, 2, 10, 22, 410, 1938, more...

integer, strictly-monotonic, +

a(n)=rad(composite(∏[p(a(n-1))]))
a(0)=1
p(n)=nth prime
∏(a)=partial products of a
composite(n)=nth composite number
rad(n)=square free kernel of n
n≥0
5 operations
Prime

Sequence rjbgtvtxr4vcm

1, 2, 10, 30, 42, 354, 2690, 52710, more...

integer, strictly-monotonic, +

a(n)=rad(composite(Δ[p(a(n-1))]))
a(0)=2
p(n)=nth prime
Δ(a)=differences of a
composite(n)=nth composite number
rad(n)=square free kernel of n
n≥0
5 operations
Prime

Sequence ukrleld251kzm

1, 2, 10, 30, 90, 270, 810, 2430, 7290, 21870, 65610, 196830, 590490, 1771470, 5314410, 15943230, 47829690, 143489070, 430467210, 1291401630, 3874204890, 11622614670, 34867844010, 104603532030, 313810596090, 941431788270, 2824295364810, 8472886094430, 25418658283290, 76255974849870, 228767924549610, 686303773648830, 2058911320946490, more...

integer, strictly-monotonic, +

a(n)=∏[p(lpf(σ(a(n-1))))]
a(0)=1
σ(n)=divisor sum of n
lpf(n)=least prime factor of n
p(n)=nth prime
∏(a)=partial products of a
n≥0
5 operations
Prime

Sequence w4rj15nwlwpkd

1, 2, 10, 130, 5590, 441610, 12806690, 1447155970, 895789545430, 1839055936767790, more...

integer, strictly-monotonic, +

a(n)=∏[p(rad(σ(a(n-1))))]
a(0)=1
σ(n)=divisor sum of n
rad(n)=square free kernel of n
p(n)=nth prime
∏(a)=partial products of a
n≥0
5 operations
Prime

Sequence 4zsmu5fpqonwm

1, 2, 12, 2, 2, 42, 12, 18, 4, 16, 108, 1018, 148, 1740, 148, 166, 396, 1486, 690, 16, 1038, 5050, 420, 276, 5856, 78, 1128, 196, 4, 810, 270, 2632, 198, 2128, 88, 7642, 72, 466, 336, 46, 13996, more...

integer, non-monotonic, +

a(n)=φ(gpf(∑[composite(a(n-1))]))
a(0)=4
composite(n)=nth composite number
∑(a)=partial sums of a
gpf(n)=greatest prime factor of n
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence 0tngl45vpoaie

1, 2, 12, 2, 2, 84, 96, 144, 8, 320, 648, 1018, 296, 1740, 1184, 2656, 792, 2972, 690, 64, 1038, 5050, 11760, 14352, 11712, 16224, 11280, 29008, 8, 3240, 6480, 31584, 57024, 51072, 880, 91704, 4032, 130480, 74592, 123648, 83976, more...

integer, non-monotonic, +

a(n)=φ(rad(∑[composite(a(n-1))]))
a(0)=4
composite(n)=nth composite number
∑(a)=partial sums of a
rad(n)=square free kernel of n
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence slj13xcdbimsp

1, 2, 12, 70, 502, 4242, 44962, more...

integer, strictly-monotonic, +

a(n)=φ(p(Δ[p(a(n-1))]))
a(0)=2
p(n)=nth prime
Δ(a)=differences of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence yf4u44t1bga0h

1, 2, 12, 112, 2212, 107440, more...

integer, strictly-monotonic, +

a(n)=φ(p(∏[p(a(n-1))]))
a(0)=1
p(n)=nth prime
∏(a)=partial products of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence 2zc5cfb4ccjjl

1, 2, 12, 224, 12406, more...

integer, strictly-monotonic, +

a(n)=Δ[φ(p(p(a(n-1))))]
a(0)=1
p(n)=nth prime
ϕ(n)=number of relative primes (Euler's totient)
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence v2deiimlg54ao

1, 2, 12, 224, 12406, 1796726, more...

integer, strictly-monotonic, +

a(n)=Δ[p(p(φ(a(n-1))))]
a(0)=2
ϕ(n)=number of relative primes (Euler's totient)
p(n)=nth prime
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence fllprkaxykcm

1, 2, 12, 252, 3528, 105840, 2222640, 31116960, 933508800, 19603684800, 274451587200, 8233547616000, 172904499936000, 2420662999104000, more...

integer, strictly-monotonic, +

a(n)=∏[rad(composite(p(a(n-1))))]
a(0)=1
p(n)=nth prime
composite(n)=nth composite number
rad(n)=square free kernel of n
∏(a)=partial products of a
n≥0
5 operations
Prime

Sequence lg4cxhnuxy3oc

1, 2, 14, 658, 449414, 7014004298, 2393199308490494, more...

integer, strictly-monotonic, +

a(n)=∏[p(σ(σ(a(n-1))))]
a(0)=1
σ(n)=divisor sum of n
p(n)=nth prime
∏(a)=partial products of a
n≥0
5 operations
Prime

Sequence hiqxisksajpmd

1, 2, 15, 142, 5523, more...

integer, strictly-monotonic, +

a(n)=rad(∑[p(p(a(n-1)))])
a(0)=1
p(n)=nth prime
∑(a)=partial sums of a
rad(n)=square free kernel of n
n≥0
5 operations
Prime

Sequence 5gf03cuz1mt0b

1, 2, 16, 256, 5120, more...

integer, strictly-monotonic, +

a(n)=φ(φ(∏[composite(a(n-1))]))
a(0)=3
composite(n)=nth composite number
∏(a)=partial products of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence pf3o2epmamhvh

1, 2, 26, 2054, 1218022, 6663798362, 417506958774386, more...

integer, strictly-monotonic, +

a(n)=∏[p(composite(σ(a(n-1))))]
a(0)=1
σ(n)=divisor sum of n
composite(n)=nth composite number
p(n)=nth prime
∏(a)=partial products of a
n≥0
5 operations
Prime

Sequence gbv1qvlfpjxpp

1, 2, 31, 2, 127, 2, 2, 2, 2, 2, 2, more...

integer, non-monotonic, +

a(n)=lpf(σ(Δ[σ(a(n-1))]))
a(0)=5
σ(n)=divisor sum of n
Δ(a)=differences of a
lpf(n)=least prime factor of n
n≥0
5 operations
Prime

Sequence rvkuvrfzkqvci

1, 2, 34, 6154, 16351178, 642486837154, more...

integer, strictly-monotonic, +

a(n)=∏[p(σ(composite(a(n-1))))]
a(0)=1
composite(n)=nth composite number
σ(n)=divisor sum of n
p(n)=nth prime
∏(a)=partial products of a
n≥0
5 operations
Prime

Sequence 3tar2fjz0m4d

1, 2, 38, 6574, 11839774, 262499629354, more...

integer, strictly-monotonic, +

a(n)=∏[p(composite(composite(a(n-1))))]
a(0)=1
composite(n)=nth composite number
p(n)=nth prime
∏(a)=partial products of a
n≥0
5 operations
Prime

Sequence gfrgmx5eaugjb

1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 5, 2, 1, 1, 2, 1, 1, 7, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, more...

integer, non-monotonic, +

a(n)=agc(σ(Δ[composite(a(n-1))]))
a(0)=3
composite(n)=nth composite number
Δ(a)=differences of a
σ(n)=divisor sum of n
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence q55zmgudhzlqg

1, 3, 1, 1, 2, 3, 9, more...

integer, non-monotonic, +

a(n)=Ω(∑[composite(p(a(n-1)))])
a(0)=2
p(n)=nth prime
composite(n)=nth composite number
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
n≥0
5 operations
Prime

Sequence hxrd3gcpy1lfh

1, 3, 1, 1, 3, 1, 3, 4, 1, 3, 3, 4, 1, 3, 3, 4, 4, 4, 3, 1, 3, 3, 1, 1, 3, 7, 1, 3, 4, 4, 3, 3, 4, 4, 1, 4, 4, 3, 3, 3, 3, 4, 3, 3, 4, 7, 4, 4, 4, 3, more...

integer, non-monotonic, +

a(n)=σ(ω(Δ[composite(a(n-1))]))
a(0)=5
composite(n)=nth composite number
Δ(a)=differences of a
ω(n)=number of distinct prime divisors of n
σ(n)=divisor sum of n
n≥0
5 operations
Prime

Sequence arm2hxwy1elen

1, 3, 1, 1, 3, 3, 3, 4, 3, 3, 3, 4, 4, 3, 4, 4, 4, 1, 3, 4, 3, 1, 3, 4, 4, 3, 4, 3, 3, 4, 3, 4, 7, 1, 4, 4, 7, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, more...

integer, non-monotonic, +

a(n)=σ(ω(Δ[composite(a(n-1))]))
a(0)=4
composite(n)=nth composite number
Δ(a)=differences of a
ω(n)=number of distinct prime divisors of n
σ(n)=divisor sum of n
n≥0
5 operations
Prime

Sequence mijksckua5ycj

1, 3, 1, 1, 3, 4, 3, 4, 3, 3, 3, 7, 3, 1, 3, 3, 7, 3, 4, 7, 1, 4, 7, 4, 7, 3, 3, 3, 4, 4, 4, more...

integer, non-monotonic, +

a(n)=σ(ω(∑[composite(a(n-1))]))
a(0)=5
composite(n)=nth composite number
∑(a)=partial sums of a
ω(n)=number of distinct prime divisors of n
σ(n)=divisor sum of n
n≥0
5 operations
Prime

Sequence 0c33bkeag45rp

1, 3, 1, 1, 5, 2, 1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 1, 5, 1, 1, 3, 1, 1, 2, 1, 2, 1, 1, 2, 1, 5, 1, 1, 3, 1, 1, 7, 2, 1, 1, 1, 6, 1, 1, 2, 1, 2, 1, 2, 15, more...

integer, non-monotonic, +

a(n)=agc(∑[lpf(σ(a(n-1)))])
a(0)=5
σ(n)=divisor sum of n
lpf(n)=least prime factor of n
∑(a)=partial sums of a
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence gfs3c1nybizzo

1, 3, 1, 1, 7, 4, 4, 6, 4, 3, 3, 6, 6, 1, 4, 6, 12, 3, 15, 7, 1, 4, 12, 7, 7, 3, 3, 4, 4, 4, 12, 6, 3, 1, 7, 3, 4, 12, 4, 1, 4, more...

integer, non-monotonic, +

a(n)=σ(Ω(∑[composite(a(n-1))]))
a(0)=5
composite(n)=nth composite number
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
σ(n)=divisor sum of n
n≥0
5 operations
Prime

Sequence vsd00qriw2vnf

1, 3, 1, 2, 1, 2, 3, more...

integer, non-monotonic, +

a(n)=τ(Ω(∑[p(a(n-1))]))
a(0)=5
p(n)=nth prime
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
τ(n)=number of divisors of n
n≥0
5 operations
Prime

Sequence c4zici1drifaj

1, 3, 1, 2, 1, 5, 2, 2, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 5, 2, 2, 3, 3, 1, 2, 1, 11, 1, 2, 1, 2, 1, 2, 1, 5, 1, 2, 1, 3, 2, 2, 1, 7, 2, 2, 1, 3, more...

integer, non-monotonic, +

a(n)=lpf(agc(∑[τ(a(n-1))]))
a(0)=4
τ(n)=number of divisors of n
∑(a)=partial sums of a
agc(n)=number of factorizations into prime powers (abelian group count)
lpf(n)=least prime factor of n
n≥0
5 operations
Prime

Sequence jq2lev2dbh35n

1, 3, 1, 2, 1, 5, 2, 2, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 5, 2, 2, 3, 3, 1, 2, 1, 11, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 2, 2, 1, 7, 2, 2, 1, 3, more...

integer, non-monotonic, +

a(n)=gpf(agc(∑[τ(a(n-1))]))
a(0)=4
τ(n)=number of divisors of n
∑(a)=partial sums of a
agc(n)=number of factorizations into prime powers (abelian group count)
gpf(n)=greatest prime factor of n
n≥0
5 operations
Prime

Sequence jmesesyddrsog

1, 3, 1, 2, 1, 5, 2, 2, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 5, 2, 2, 3, 3, 1, 2, 1, 11, 1, 2, 1, 6, 1, 2, 1, 5, 1, 2, 1, 3, 2, 2, 1, 7, 2, 2, 1, 3, more...

integer, non-monotonic, +

a(n)=rad(agc(∑[τ(a(n-1))]))
a(0)=4
τ(n)=number of divisors of n
∑(a)=partial sums of a
agc(n)=number of factorizations into prime powers (abelian group count)
rad(n)=square free kernel of n
n≥0
5 operations
Prime

Sequence ngigqdt4chhik

1, 3, 1, 2, 3, 4, 4, more...

integer, non-monotonic, +

a(n)=Ω(∑[p(σ(a(n-1)))])
a(0)=5
σ(n)=divisor sum of n
p(n)=nth prime
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
n≥0
5 operations
Prime

Sequence zaksjp4zcivgb

1, 3, 1, 3, 1, 1, 5, 30, more...

integer, non-monotonic, +

a(n)=agc(∑[p(gpf(a(n-1)))])
a(0)=4
gpf(n)=greatest prime factor of n
p(n)=nth prime
∑(a)=partial sums of a
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence 0awvguc200hej

1, 3, 1, 3, 2, 3, 3, 1, 5, 3, 3, 3, 2, 3, 2, 1, 1, 1, 1, 1, 1, 2, 3, 5, 2, 6, 1, 2, 5, 1, 1, 1, more...

integer, non-monotonic, +

a(n)=agc(gpf(∑[composite(a(n-1))]))
a(0)=5
composite(n)=nth composite number
∑(a)=partial sums of a
gpf(n)=greatest prime factor of n
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence 2dsvlksf4lupc

1, 3, 1, 3, 2, 4, 3, 3, 5, 4, 1, 4, 3, 5, 5, 5, 2, 4, 3, 3, 3, 5, 2, 5, 4, 5, 5, 4, 2, 4, 4, 3, 6, 5, 2, 3, 6, 5, 2, 4, 5, 5, 4, 5, 7, 5, 3, 4, 3, 4, more...

integer, non-monotonic, +

a(n)=Ω(σ(∑[τ(a(n-1))]))
a(0)=4
τ(n)=number of divisors of n
∑(a)=partial sums of a
σ(n)=divisor sum of n
Ω(n)=number of prime divisors of n
n≥0
5 operations
Prime

Sequence 0hj5ose3qw4yj

1, 3, 1, 3, 4, 3, 4, 5, 2, 5, 5, 6, 5, 5, 4, 6, 7, 4, 3, 3, 6, 6, 5, 2, 5, 8, 3, 6, 7, 7, 6, 5, 9, 8, 4, 7, 5, 6, 7, 4, 4, 10, 5, 8, 6, 9, 8, 5, 8, 4, more...

integer, non-monotonic, +

a(n)=Ω(σ(Δ[composite(a(n-1))]))
a(0)=5
composite(n)=nth composite number
Δ(a)=differences of a
σ(n)=divisor sum of n
Ω(n)=number of prime divisors of n
n≥0
5 operations
Prime

Sequence yba3h2xodz12l

1, 3, 1, 3, 4, 13, 28, 31, 31, 31, 60, 39, 31, 31, more...

integer, non-monotonic, +

a(n)=σ(τ(Δ[σ(a(n-1))]))
a(0)=3
σ(n)=divisor sum of n
Δ(a)=differences of a
τ(n)=number of divisors of n
n≥0
5 operations
Prime

Sequence qsirpjotnfgyk

1, 3, 1, 3, 5, 17, 71, 97, 617, 347, 401, 563, 13721, 61, more...

integer, non-monotonic, +

a(n)=gpf(composite(Δ[σ(a(n-1))]))
a(0)=3
σ(n)=divisor sum of n
Δ(a)=differences of a
composite(n)=nth composite number
gpf(n)=greatest prime factor of n
n≥0
5 operations
Prime

Sequence wcjahdecjzrch

1, 3, 1, 3, 7, 5, 2, 2, 1, 1, 6, 1, 1, 1, 6, 1, 3, 3, 1, 2, 2, 1, 1, 1, 1, 11, 2, 2, 3, 1, 1, 3, 2, more...

integer, non-monotonic, +

a(n)=agc(p(Δ[composite(a(n-1))]))
a(0)=3
composite(n)=nth composite number
Δ(a)=differences of a
p(n)=nth prime
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence gcxjemq3e4f2b

1, 3, 1, 3, 7, 12, 4, 3, 1, 4, 4, 3, 4, 3, 8, 3, 15, 3, 3, 7, 12, 3, 1, 3, 7, 3, 7, 4, 4, 18, 6, 3, 6, 1, 1, 6, 12, 1, 3, 4, 3, 4, more...

integer, non-monotonic, +

a(n)=σ(Ω(∑[composite(a(n-1))]))
a(0)=3
composite(n)=nth composite number
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
σ(n)=divisor sum of n
n≥0
5 operations
Prime

Sequence ba3izkkq5ed0o

1, 3, 1, 4, 1, 1, 1, 1, 1, 1, more...

integer, non-monotonic, +

a(n)=σ(agc(Δ[σ(a(n-1))]))
a(0)=3
σ(n)=divisor sum of n
Δ(a)=differences of a
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence zqrhyrm3ajx1c

1, 3, 1, 4, 1, 3, 3, 7, 1, 4, 1, 4, 3, 3, 1, 7, 3, 3, 4, 4, 1, 4, 1, 6, 3, 3, 3, 7, 1, 3, 3, 7, 1, 4, 1, 4, 4, 3, 1, 6, 3, 4, 3, 4, 1, 7, 3, 7, 3, 3, more...

integer, non-monotonic, +

a(n)=σ(Ω(∑[φ(a(n-1))]))
a(0)=5
ϕ(n)=number of relative primes (Euler's totient)
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
σ(n)=divisor sum of n
n≥0
5 operations
Prime

Sequence tjtwyojs2j4ro

1, 3, 1, 4, 2, 4, 16, 32, 40, 48, 64, 96, 96, 100, more...

integer, non-monotonic, +

a(n)=τ(σ(Δ[σ(a(n-1))]))
a(0)=3
σ(n)=divisor sum of n
Δ(a)=differences of a
τ(n)=number of divisors of n
n≥0
5 operations
Prime

Sequence nxzozz0qhgwnn

1, 3, 1, 11, 1, 1, more...

integer, non-monotonic, +

a(n)=agc(∑[p(σ(a(n-1)))])
a(0)=2
σ(n)=divisor sum of n
p(n)=nth prime
∑(a)=partial sums of a
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence kakkb1wul2yk

1, 3, 1, 12, 12, 28, 91, 252, 992, 2286, 12240, 10800, 61200, 80352, more...

integer, non-monotonic, +

a(n)=σ(φ(Δ[σ(a(n-1))]))
a(0)=3
σ(n)=divisor sum of n
Δ(a)=differences of a
ϕ(n)=number of relative primes (Euler's totient)
n≥0
5 operations
Prime

Sequence jlua2xy1dsm2o

1, 3, 2, 1, 2, 3, 3, 1, 2, 3, 3, 2, 2, 2, 4, 1, 3, 5, 3, 1, 2, 2, 4, 3, 2, 3, 3, 1, 3, 3, 5, 1, 2, 4, 4, 2, 2, 3, 4, 1, 3, 5, 3, 1, 2, 2, 5, 2, 3, 7, more...

integer, non-monotonic, +

a(n)=Ω(∑[gpf(σ(a(n-1)))])
a(0)=5
σ(n)=divisor sum of n
gpf(n)=greatest prime factor of n
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
n≥0
5 operations
Prime

Sequence k2bh44re3akuj

1, 3, 2, 2, 1, 1, 2, 2, 3, 3, 1, 2, 1, 7, 2, 3, 1, 1, 1, 2, 1, 5, 3, 2, 3, 2, 2, 2, 1, 3, 1, 2, 3, 6, 1, 1, 2, 5, 2, 2, 2, 1, 2, 1, 7, 2, 2, 2, 1, 3, more...

integer, non-monotonic, +

a(n)=agc(gpf(∑[τ(a(n-1))]))
a(0)=4
τ(n)=number of divisors of n
∑(a)=partial sums of a
gpf(n)=greatest prime factor of n
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence tnkpotelxnjsd

1, 3, 2, 2, 1, 2, 2, 2, 2, 3, 1, 2, 1, 7, 2, 1, 1, 2, 1, 2, 2, 5, 3, 2, 3, 1, 2, 2, 1, 2, 1, 2, 2, 6, 1, 2, 3, 5, 2, 2, 1, 2, 2, 3, 2, 1, 2, 2, 1, 3, more...

integer, non-monotonic, +

a(n)=agc(lpf(∑[τ(a(n-1))]))
a(0)=4
τ(n)=number of divisors of n
∑(a)=partial sums of a
lpf(n)=least prime factor of n
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence xznqiefwgb3ab

1, 3, 2, 2, 1, 5, 2, 2, 1, 3, 1, 2, 1, 7, 1, 4, 1, 3, 1, 2, 5, 5, 3, 2, 3, 3, 1, 2, 1, 1, 1, 2, 1, 6, 1, 5, 1, 5, 2, 2, 1, 3, 2, 2, 1, 7, 2, 1, 1, 3, more...

integer, non-monotonic, +

a(n)=agc(rad(∑[τ(a(n-1))]))
a(0)=4
τ(n)=number of divisors of n
∑(a)=partial sums of a
rad(n)=square free kernel of n
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence hh5haimgonalm

1, 3, 2, 2, 1, 6, 1, 5, 5, 2, 2, 2, 2, more...

integer, non-monotonic, +

a(n)=agc(p(∑[composite(a(n-1))]))
a(0)=3
composite(n)=nth composite number
∑(a)=partial sums of a
p(n)=nth prime
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence jjzpjrlbaqnzp

1, 3, 2, 2, 2, 3, 2, 5, more...

integer, non-monotonic, +

a(n)=Ω(∑[p(φ(a(n-1)))])
a(0)=5
ϕ(n)=number of relative primes (Euler's totient)
p(n)=nth prime
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
n≥0
5 operations
Prime

Sequence o530o2frv2vbm

1, 3, 2, 2, 6, 2, 2, more...

integer, non-monotonic, +

a(n)=Ω(∑[composite(p(a(n-1)))])
a(0)=3
p(n)=nth prime
composite(n)=nth composite number
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
n≥0
5 operations
Prime

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