A002589 -id:A002589 - cp's OEIS frontend

A046798 Number of divisors of 2^n + 1.

2, 2, 2, 3, 2, 4, 4, 4, 2, 8, 6, 4, 4, 4, 8, 12, 2, 4, 16, 4, 4, 12, 8, 4, 8, 16, 16, 20, 4, 8, 48, 4, 4, 24, 16, 32, 16, 8, 16, 12, 4, 8, 64, 4, 8, 64, 32, 8, 8, 8, 64, 48, 8, 8, 64, 48, 8, 24, 8, 16, 16, 4, 32, 64, 4, 64, 64, 8, 12, 24, 96, 8, 32, 8, 32, 96, 16, 64, 768, 4, 8, 192, 32, 64

Offset: 0

Labos Elemer

nonn

a(n) is odd iff n = 3, as a consequence of the Catalan-Mihăilescu theorem. - Bernard Schott, Oct 05 2021

			a(7)=4, because 2^7 + 1 = 129 has 4 divisors.

Max Alekseyev, Table of n, a(n) for n = 0..1128 (terms 0..500 from T. D. Noe, terms 501..1062 from Amiram Eldar, term 1108 from Tyler Busby)
Wikipedia, Catalan's conjecture.

Cf. A000005, A000051, A002587, A002589, A046801, A054992, A057957, A059886, A274906, A344897.

[NumberOfDivisors(2^n+1): n in [0..100]]; // Vincenzo Librandi, Feb 05 2018

a:= n-> numtheory[tau](2^n+1):
seq(a(n), n=0..100);  # Alois P. Heinz, Aug 23 2021

A046798[n_IntegerQ]:=DivisorSigma[0,1+2^n]; (* Enrique Pérez Herrero, Nov 09 2010 *)
DivisorSigma[0, 1 + 2^#] & /@ Range[0, 83] (* Jayanta Basu, Jun 29 2013 *)
Table[DivisorSigma[0, 2^n + 1], {n, 0, 100}] (* Vincenzo Librandi, Feb 05 2018 *)

a(n) = numdiv(2^n+1); \\ Michel Marcus, Mar 18 2017

from sympy.ntheory import divisor_count
def A046798(n): return divisor_count(2**n + 1) # Indranil Ghosh, Mar 18 2017

a(n) = A000005(A000051(n)). - Michel Marcus, Mar 18 2017

A069061 Sum of divisors of 2^n+1.

Original entry on oeis.org

4, 6, 13, 18, 48, 84, 176, 258, 800, 1302, 2736, 4356, 10928, 20520, 51792, 65538, 174768, 351120, 699056, 1110276, 3100240, 5048232, 11184816, 17041416, 49012992, 82623888, 211053040, 284225796, 727960800, 1494039792, 2863311536, 4301668356, 12611914848, 20788904016

Offset: 1

Benoit Cloitre, Apr 04 2002

nonn

Max Alekseyev, Table of n, a(n) for n = 1..1128 (terms 1..1062 from Amiram Eldar)

Cf. A000051, A000203, A002185, A002587, A002589, A046798, A046799, A053285, A054992, A057957, A059886, A085029, A086257, A112092, A250291, A274906, A295501.

Row sums of A374237.

DivisorSigma[1, 2^Range[50] + 1] (* Paolo Xausa, Jul 05 2024 *)

a(n) = sigma(2^n+1); \\ Michel Marcus, Nov 24 2013

a(n) = sigma(2^n+1).

a(n) = A000203(A000051(n)). - Michel Marcus, Nov 24 2013

More terms from Amiram Eldar, Oct 04 2019

A002185 Smallest primitive factor of 2^(2n+1) + 1.

Original entry on oeis.org

3, 1, 11, 43, 19, 683, 2731, 331, 43691, 174763, 5419, 2796203, 251, 87211, 59, 715827883, 67, 281, 1777, 22366891, 83, 2932031007403, 18837001, 283, 4363953127297, 307, 107, 2971, 571, 2833, 768614336404564651, 77158673929, 131, 7327657, 139, 56409643, 1753

Offset: 0

N. J. A. Sloane

nonn

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. 85.
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).

Max Alekseyev, Table of n, a(n) for n = 0..568
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
S. S. Wagstaff, Jr., The Cunningham Project

Cf. A002589, A086257, A112927.

Terms a(25) onward from Max Alekseyev, Oct 16 2022

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A046798 Number of divisors of 2^n + 1.

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A069061 Sum of divisors of 2^n+1.

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A002185 Smallest primitive factor of 2^(2n+1) + 1.

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