A227575 -id:A227575 - cp's OEIS frontend

A274903 Largest prime factor of 4^n + 1.

2, 5, 17, 13, 257, 41, 241, 113, 65537, 109, 61681, 2113, 673, 1613, 15790321, 1321, 6700417, 26317, 38737, 525313, 4278255361, 14449, 2931542417, 30269, 22253377, 268501, 308761441, 279073, 54410972897, 536903681, 4562284561, 384773, 67280421310721

Offset: 0

Vincenzo Librandi, Jul 11 2016

nonn

			4^3 + 1 = 65 = 5*13, so a(3) = 13.

Max Alekseyev, Table of n, a(n) for n = 0..583
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

Cf. largest prime factor of k^n+1: A002587 (k=2), A074476 (k=3), this sequence (k=4), A074478 (k=5), A274904 (k=6), A227575 (k=7), A274905 (k=8), A002592 (k=9), A003021 (k=10), A062308 (k=11).

Cf. A006530, A052539.

[Maximum(PrimeDivisors(4^n+1)): n in [0..35]];

Table[FactorInteger[4^n + 1][[-1, 1]], {n, 0, 30}]

a(n)=my(f=factor(4^n+1)[,1]); f[#f] \\ Charles R Greathouse IV, Jul 12 2016

a(n) = A006530(A052539(n)). - Michel Marcus, Jul 11 2016
a(2n) = A002590(n). a(2n+1) = A229747(n). - R. J. Mathar, Feb 28 2018
a(n) = A002587(2*n). - Amiram Eldar, Feb 01 2020

Terms to a(100) in b-file from  Vincenzo Librandi, Jul 12 2016
a(101)-a(531) in b-file from Amiram Eldar, Feb 01 2020
a(532)-a(583) in b-file from Max Alekseyev, Apr 25 2022, Mar 15 2025

A057937 Number of prime factors of 7^n + 1 (counted with multiplicity).

Original entry on oeis.org

3, 3, 4, 2, 5, 5, 5, 3, 5, 6, 5, 5, 5, 4, 7, 3, 4, 6, 5, 4, 8, 6, 4, 4, 6, 5, 6, 6, 4, 10, 6, 4, 8, 6, 11, 8, 5, 4, 9, 6, 7, 7, 10, 5, 12, 7, 4, 6, 12, 11, 8, 5, 7, 9, 13, 8, 9, 7, 7, 9, 4, 6, 14, 4, 9, 12, 6, 5, 8, 10, 5, 9, 6, 4, 11, 7, 12, 10, 7, 6, 10, 6, 5, 12, 8, 6, 8, 5, 8, 14, 11, 6, 9, 6, 11

Offset: 1

Patrick De Geest, Oct 15 2000

nonn

Max Alekseyev, Table of n, a(n) for n = 1..387 (first 372 terms from Amiram Eldar)
S. S. Wagstaff, Jr., The Cunningham Project

bigomega(b^n+1): A057934 (b=10), A057935 (b=9), A057936 (b=8), this sequence (b=7), A057938 (b=6), A057939 (b=5), A057940 (b=4), A057941 (b=3), A054992 (b=2).

Cf. A001222, A034491, A057954, A227575.

f:=func; [f(7^n + 1):n in [1..110]]; // Marius A. Burtea, Feb 02 2020

PrimeOmega[Table[7^n + 1, {n, 1, 30}]] (* Amiram Eldar, Feb 02 2020 *)

a(n) = A057954(2n) - A057954(n). - T. D. Noe, Jun 19 2003

a(n) = A001222(A034491(n)). - Amiram Eldar, Feb 02 2020

A074478 Largest prime factor of 5^n + 1.

Original entry on oeis.org

2, 3, 13, 7, 313, 521, 601, 449, 11489, 5167, 9161, 5281, 390001, 38923, 234750601, 7621, 29423041, 41540861, 6597973, 213029, 632133361, 7603, 1030330938209, 42272797713043, 152587500001, 50150933101, 83181652304609, 16018507

Offset: 0

Rick L. Shepherd, Aug 23 2002

nonn

			5^11 + 1 = 48828126 = 2*3*23*67*5281, so a(11) = 5281.

Table of n, a(n) for n = 0..471
S. S. Wagstaff, Jr., The Cunningham Project

Cf. A002587 (largest prime factor of 2^n + 1), A074479 (largest prime factor of 5^n - 1), A074476 (largest prime factor of 3^n + 1), A227575 (largest prime factor of 7^n + 1).

Cf. A006530, A034474.

[Maximum(PrimeDivisors(5^n+1)): n in [0..30]]; // Vincenzo Librandi, Jul 09 2016

Table[FactorInteger[5^n + 1][[-1, 1]], {n, 0, 30}] (* Bruno Berselli, Aug 23 2013 *)

for(n=0,30, v=factor(5^n+1); print1(v[matsize(v)[1],1],","))

a(n) = A006530(A034474(n)). - Michel Marcus, Jul 09 2016

Terms to a(100) in b-file from Vincenzo Librandi, Jul 09 2016
a(101)-a(451) in b-file from Amiram Eldar, Feb 01 2020
a(452)-a(471) in b-file from Max Alekseyev, Apr 25 2022, Jan 04 2024

A366638 Sum of the divisors of 7^n+1.

Original entry on oeis.org

3, 15, 93, 660, 3606, 34560, 236964, 1559520, 9155916, 77423280, 530807472, 3868683120, 21224771760, 185094572580, 1261494915594, 9988783073280, 49990612274316, 436182213726030, 3279858902194056, 21372989348391720, 122709716651985624, 1082323574100172800

Offset: 0

Sean A. Irvine, Oct 15 2023

nonn

			a(4)=3606 because 7^4+1 has divisors {1, 2, 1201, 2402}.

Max Alekseyev, Table of n, a(n) for n = 0..387

Cf. A034491, A000203, A057937, A227575, A366634, A366636, A366637, A366639.

Cf. A069061, A366578, A366607, A366617, A366629, A366657, A366666, A366668, A366689, A366715.

a:=n->numtheory[sigma](7^n+1):
seq(a(n), n=0..100);

DivisorSigma[1, 7^Range[0, 21] + 1] (* Paul F. Marrero Romero, Oct 16 2023 *)

a(n) = sigma(7^n+1) = A000203(A034491(n)).

A366639 a(n) = phi(7^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 4, 20, 168, 1200, 7600, 43200, 407680, 2712832, 19707408, 112560000, 945677920, 6768230400, 47530457728, 271289229120, 2096760960000, 16569393144832, 116315256993600, 597938524646400, 5699431359135360, 38890647857280000, 270061302781670400

Offset: 0

Sean A. Irvine, Oct 15 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..387

Cf. A034491, A000010, A057937, A227575, A366635, A366636, A366637, A366638.

Cf. A053285, A366579, A366608, A366618, A366630, A366658, A366667, A366669, A366690, A366716.

EulerPhi[7^Range[0,21] + 1] (* Paul F. Marrero Romero, Nov 05 2023 *)

PARI
```
{a(n) = eulerphi(7^n+1)}
```

a(n) = A000010(A034491(n)). - Paul F. Marrero Romero, Nov 06 2023

A366636 Number of distinct prime divisors of 7^n + 1.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 4, 3, 3, 3, 4, 3, 5, 3, 3, 5, 3, 2, 5, 3, 4, 6, 5, 2, 4, 4, 4, 4, 6, 2, 8, 4, 4, 6, 5, 9, 8, 3, 3, 7, 6, 5, 6, 8, 5, 10, 6, 2, 6, 10, 8, 6, 5, 5, 8, 10, 8, 7, 6, 5, 9, 2, 5, 12, 4, 7, 11, 4, 5, 6, 8, 3, 9, 4, 3, 9, 7, 10, 8, 5, 6, 8, 5, 3, 12

Offset: 0

Sean A. Irvine, Oct 15 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..387

Cf. A034491, A001221, A057937, A227575, A366632, A366637, A366638, A366639.

Cf. A046799, A366580, A366605, A366615, A366627, A366655, A366664, A119704, A366686, A366712.

PrimeNu[7^Range[0,84] + 1] (* Paul F. Marrero Romero, Nov 11 2023 *)

for(n = 0, 100, print1(omega(7^n + 1), ", "))

a(n) = omega(7^n+1) = A001221(A034491(n)).

A366637 Number of divisors of 7^n+1.

Original entry on oeis.org

2, 4, 6, 8, 4, 16, 24, 16, 8, 16, 32, 16, 32, 16, 12, 64, 8, 8, 48, 16, 16, 128, 48, 8, 16, 32, 24, 32, 64, 8, 512, 32, 16, 128, 48, 1024, 256, 16, 12, 256, 64, 64, 96, 512, 32, 2048, 96, 8, 64, 2048, 640, 128, 32, 64, 384, 3072, 256, 256, 96, 64, 512, 8, 48

Offset: 0

Sean A. Irvine, Oct 15 2023

nonn

			a(4)=4 because 7^4+1 has divisors {1, 2, 1201, 2402}.

Max Alekseyev, Table of n, a(n) for n = 0..387

Cf. A034491, A000005, A057937, A227575, A366633, A366636, A366638, A366639.

Cf. A046798, A366577, A366606, A366616, A366628, A366656, A366665, A344897, A366688, A366714.

a:=n->numtheory[tau](7^n+1):
seq(a(n), n=0..100);

DivisorSigma[0, 7^Range[0, 62] + 1] (* Paul F. Marrero Romero, Oct 16 2023 *)

PARI
```
a(n) = numdiv(7^n+1);
```

a(n) = sigma0(7^n+1) = A000005(A034491(n)).

A366720 Largest prime factor of 12^n+1.

Original entry on oeis.org

2, 13, 29, 19, 233, 19141, 20593, 13063, 260753, 1801, 85403261, 57154490053, 2227777, 222379, 13156924369, 35671, 1200913648289, 66900193189411, 122138321401, 905265296671, 67657441, 1885339, 68368660537, 49489630860836437, 592734049, 438472201

Offset: 0

Sean A. Irvine, Oct 17 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..306

Cf. A178248, A006530, A002587, A074476, A274903, A074478, A274904, A227575, A274905, A002592, A003021, A062308, A002590, A366712, A366713, A366714, A366715, A366716, A366717, A366718, A366719, A324941.

Table[FactorInteger[12^n + 1][[-1, 1]], {n, 0, 20}]

a(n) = A006530(A178248(n)). - Paul F. Marrero Romero, Dec 07 2023

A324941 Largest prime factor of 17^n + 1.

Original entry on oeis.org

2, 3, 29, 13, 41761, 101, 83233, 22796593, 184417, 5653, 63541, 87415373, 72337, 2001793, 100688449, 238212511, 52548582913, 45957792327018709121, 382069, 20352763, 1186844128302568601, 88109799136087, 6901823633, 1109309383381084655697725873, 48661191868691111041

Offset: 0

Vincenzo Librandi, Apr 05 2019

nonn

Max Alekseyev, Table of n, a(n) for n = 0..211

Cf. A006530, A224384.

Cf. A002587, A074476, A274903, A074478, A274904, A227575, A274905, A002592, A003021, A062308, A002590.

[Maximum(PrimeDivisors(17^n + 1)): n in [0..40]];

Table[FactorInteger[17^n + 1] [[-1,1]], {n, 0, 30}]

a(n) = vecmax(factor(17^n+1)[, 1]); \\ Jinyuan Wang, Apr 05 2019

a(n) = A006530(A224384(n)).

cp's OEIS Frontend

A274903 Largest prime factor of 4^n + 1.

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A057937 Number of prime factors of 7^n + 1 (counted with multiplicity).

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A074478 Largest prime factor of 5^n + 1.

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A366638 Sum of the divisors of 7^n+1.

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A366639 a(n) = phi(7^n+1), where phi is Euler's totient function (A000010).

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A366636 Number of distinct prime divisors of 7^n + 1.

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Mathematica

PARI

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A366637 Number of divisors of 7^n+1.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula