cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A274903 Largest prime factor of 4^n + 1.

Original entry on oeis.org

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

Views

Author

Vincenzo Librandi, Jul 11 2016

Keywords

Examples

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

Links

Crossrefs

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.

Programs

  • Magma
    [Maximum(PrimeDivisors(4^n+1)): n in [0..35]];
  • Mathematica
    Table[FactorInteger[4^n + 1][[-1, 1]], {n, 0, 30}]
  • PARI
    a(n)=my(f=factor(4^n+1)[,1]); f[#f] \\ Charles R Greathouse IV, Jul 12 2016

Formula

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

Extensions

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

A366690 a(n) = phi(11^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 4, 60, 432, 7320, 53680, 803520, 6495720, 100874752, 764738496, 12756110400, 89493288192, 1568774615040, 11278053084480, 180228847518720, 1310982643872000, 22974417331646464, 168479281019744640, 2521788545778163200, 20190830281379049600
Offset: 0

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Links

Crossrefs

Cf. A034524, A000010, A062308, A366685, A366686, A366687, A366689, A366689, A366716.

Programs

  • Mathematica
    EulerPhi[11^Range[0,19] + 1] (* Paul F. Marrero Romero, Nov 10 2023 *)
  • PARI
    {a(n) = eulerphi(11^n+1)}

Formula

a(n) = A000010(A034524(n)). - Paul F. Marrero Romero, Nov 10 2023

A366688 Number of divisors of 11^n+1.

Original entry on oeis.org

2, 6, 4, 18, 4, 12, 16, 12, 8, 48, 8, 96, 16, 48, 32, 144, 8, 48, 32, 96, 16, 72, 16, 96, 128, 48, 8, 240, 64, 48, 64, 96, 16, 4608, 64, 1152, 128, 24, 16, 1152, 32, 48, 512, 24, 64, 3072, 64, 96, 32, 192, 64, 1152, 8, 96, 512, 6144, 128, 2304, 64, 96, 256, 48
Offset: 0

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Examples

			a(4)=4 because 11^4+1 has divisors {1, 2, 7321, 14642}.

Links

Crossrefs

Cf. A034524, A000005, A062308, A366683, A366686, A366687, A366689, A366690.
Cf. A046798, A344897, A366714.

Programs

  • Maple
    a:=n->numtheory[tau](11^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[0,11^Range[0,70]+1] (* Harvey P. Dale, Mar 17 2025 *)
  • PARI
    a(n) = numdiv(11^n+1);

Formula

a(n) = sigma0(11^n+1) = A000005(A034524(n)).

A366687 Number of prime factors of 11^n + 1 (counted with multiplicity).

Original entry on oeis.org

1, 3, 2, 5, 2, 4, 4, 4, 3, 7, 3, 7, 4, 6, 5, 8, 3, 6, 5, 7, 4, 7, 4, 7, 7, 6, 3, 10, 6, 6, 6, 7, 4, 13, 6, 11, 7, 5, 4, 11, 5, 6, 9, 5, 6, 13, 6, 7, 5, 8, 6, 11, 3, 7, 9, 13, 7, 12, 6, 7, 8, 6, 4, 13, 3, 10, 8, 9, 7, 14, 8, 6, 10, 8, 8, 13, 6, 12, 12, 7, 10
Offset: 0

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Links

Crossrefs

Cf. A034524, A001222, A057934, A062308, A366686, A366688, A366689, A366690.
Cf. A054992, A057941, A057940, A057939, A057938, A057937, A057936, A057935, A057934, A366713.

Programs

  • Mathematica
    PrimeOmega[11^Range[70]+1]
  • PARI
    a(n)=bigomega(11^n+1)

Formula

a(n) = bigomega(11^n+1) = A001222(A034524(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

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

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

Programs

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

Formula

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

Views

Author

Vincenzo Librandi, Apr 05 2019

Keywords

Links

Crossrefs

Cf. A006530, A224384.
Cf. A002587, A074476, A274903, A074478, A274904, A227575, A274905, A002592, A003021, A062308, A002590.

Programs

  • Magma
    [Maximum(PrimeDivisors(17^n + 1)): n in [0..40]];
  • Mathematica
    Table[FactorInteger[17^n + 1] [[-1,1]], {n, 0, 30}]
  • PARI
    a(n) = vecmax(factor(17^n+1)[, 1]); \\ Jinyuan Wang, Apr 05 2019

Formula

a(n) = A006530(A224384(n)).
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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