A274904 -id:A274904 - 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

A057938 Number of prime factors of 6^n + 1 (counted with multiplicity).

Original entry on oeis.org

1, 1, 2, 1, 3, 3, 4, 2, 3, 3, 2, 2, 4, 3, 5, 3, 3, 6, 3, 3, 6, 4, 3, 4, 4, 4, 5, 5, 4, 9, 2, 3, 6, 3, 11, 5, 4, 3, 9, 5, 4, 7, 2, 3, 7, 5, 2, 7, 7, 6, 8, 4, 5, 10, 8, 6, 7, 3, 2, 6, 3, 2, 10, 3, 8, 11, 5, 5, 6, 7, 4, 5, 6, 5, 10, 5, 6, 11, 6, 6, 8, 4, 5, 8, 8, 5, 11, 4, 3, 16, 12, 4, 5, 5, 10, 4, 4, 5

Offset: 1

Patrick De Geest, Oct 15 2000

nonn

Max Alekseyev, Table of n, a(n) for n = 1..430 (first 408 terms from Amiram Eldar)
S. S. Wagstaff, Jr., The Cunningham Project

bigomega(b^n+1): A057934 (b=10), A057935 (b=9), A057936 (b=8), A057937 (b=7), this sequence (b=6), A057939 (b=5), A057940 (b=4), A057941 (b=3), A054992 (b=2).

Cf. A001222, A057955, A062394, A274904.

f:=func; [f(6^n + 1):n in [1..100]]; // Marius A. Burtea, Feb 02 2020

PrimeOmega[6^Range[100]+1] (* Harvey P. Dale, Mar 10 2013 *)

a(n) = A057955(2n) - A057955(n). - T. D. Noe, Jun 19 2003

a(n) = A001222(A062394(n)). - Amiram Eldar, Feb 02 2020

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

A366670 Smallest prime dividing 6^n + 1.

Original entry on oeis.org

2, 7, 37, 7, 1297, 7, 13, 7, 17, 7, 37, 7, 1297, 7, 37, 7, 353, 7, 13, 7, 41, 7, 37, 7, 17, 7, 37, 7, 281, 7, 13, 7, 2753, 7, 37, 7, 577, 7, 37, 7, 17, 7, 13, 7, 89, 7, 37, 7, 193, 7, 37, 7, 1297, 7, 13, 7, 17, 7, 37, 7, 41, 7, 37, 7, 4926056449, 7, 13, 7, 137

Offset: 0

Sean A. Irvine, Oct 15 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..4095

Cf. A020639, A062394, A274904, A366630.

Cf. A002586, A366609, A366671, A038371, A366719.

Table[FactorInteger[6^n + 1][[1,1]], {n, 0, 68}] (* Paul F. Marrero Romero, Oct 17 2023 *)

a(n) = A020639(A062394(n)). - Paul F. Marrero Romero, Oct 17 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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A057938 Number of prime factors of 6^n + 1 (counted with multiplicity).

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A366720 Largest prime factor of 12^n+1.

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A366670 Smallest prime dividing 6^n + 1.

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A324941 Largest prime factor of 17^n + 1.

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