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.

Previous Showing 11-14 of 14 results.

A366575 Number of divisors of 3^n - 1.

Original entry on oeis.org

2, 4, 4, 10, 6, 16, 4, 24, 8, 24, 8, 80, 4, 16, 24, 112, 8, 128, 8, 180, 16, 64, 8, 384, 24, 16, 64, 160, 16, 768, 16, 256, 32, 128, 48, 1280, 8, 64, 96, 864, 16, 768, 8, 640, 384, 32, 32, 14336, 128, 384, 64, 160, 16, 4096, 128, 1536, 128, 256, 8, 23040, 8
Offset: 1

Views

Author

Sean A. Irvine, Oct 13 2023

Keywords

Examples

			a(4)=10 because 3^4-1 has divisors {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}.

Links

Crossrefs

Cf. A024023, A000005, A046801, A133801, A295500, A366576.
Cf. A046801, A366602, A366612, A366621, A366633, A366652, A366661, A070528, A366683, A366709.

Programs

  • Maple
    a:=n->numtheory[tau](3^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[0,3^Range[100]-1] (* Paolo Xausa, Oct 15 2023 *)

Formula

a(n) = sigma0(3^n-1) = A000005(A024023).

A366576 Sum of the divisors of 3^n-1.

Original entry on oeis.org

3, 15, 42, 186, 399, 1680, 3282, 15876, 31836, 123690, 277344, 1541568, 2391486, 8992680, 25483332, 111757968, 193819392, 967814400, 1744488660, 9366647892, 16912999320, 62424587520, 144219337920, 852903426816, 1397135488896, 4766016364260, 12477973754400
Offset: 1

Views

Author

Sean A. Irvine, Oct 13 2023

Keywords

Examples

			a(4)=186 because 3^4-1 has divisors {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}.

Links

Crossrefs

Cf. A024023, A000203, A075708, A133801, A295500, A366575.
Cf. A075708, A366603, A366613, A366622, A366634, A366653, A366662, A102146, A366684, A366710.

Programs

  • Maple
    a:=n->numtheory[sigma](3^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[1,3^Range[30]-1] (* Paolo Xausa, Oct 15 2023 *)

Formula

a(n) = sigma(3^n-1) = A000203(A024023).

A366611 Number of distinct prime divisors of 5^n - 1.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 2, 4, 4, 5, 2, 6, 2, 5, 6, 6, 3, 7, 4, 8, 5, 6, 3, 8, 7, 5, 8, 7, 4, 11, 3, 8, 5, 6, 8, 11, 4, 8, 5, 11, 3, 12, 3, 9, 11, 6, 2, 11, 3, 11, 7, 8, 4, 14, 8, 9, 6, 7, 3, 17, 4, 7, 10, 11, 7, 12, 6, 11, 8, 14, 3, 16, 4, 8, 15, 11, 6, 11, 4, 15
Offset: 1

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

Cf. A024049, A001221, A057956, A059887, A074479, A143665, A218357, A295502, A366612, A366613.
Cf. A046800, A133801, A366604, A366620, A366632, A366651, A366660, A102347, A366681, A366707.

Programs

  • PARI
    for(n = 1, 100, print1(omega(5^n - 1), ", "))

Formula

a(n) = omega(5^n-1) = A001221(A024049(n)).

A002591 Largest prime factor of 3^(2n+1) - 1.

Original entry on oeis.org

2, 13, 11, 1093, 757, 3851, 797161, 4561, 34511, 363889, 368089, 1001523179, 391151, 8209, 20381027, 4404047, 2413941289, 2664097031, 17189128703, 797161, 86950696619, 380808546861411923, 927001, 96656723, 131713, 99810171997
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
  • M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 2, p. 28.
  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Together with A274909 forms bisection of A074477.Cf. A057958, A059885, A085028, A133801, A235366.

Programs

  • Mathematica
    Table[FactorInteger[3^(2n-1)-1][[-1,1]],{n,30}] (* Harvey P. Dale, Oct 19 2022 *)

Formula

a(n) = A074477(2n+1). - Max Alekseyev, May 22 2022

Extensions

Corrected and extended by Jud McCranie, Jan 03 2001
Terms up to a(307) in b-file from Sean A. Irvine, Apr 20 2014
a(0) prepended and a(308)-a(344) added to b-file by Max Alekseyev, Apr 24 2019, Sep 10 2020, Aug 26 2021, May 22 2022
Previous Showing 11-14 of 14 results.

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

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