A195051 Number of divisors of 24*n - 1.

2, 2, 2, 4, 4, 4, 2, 2, 4, 2, 2, 4, 2, 4, 2, 2, 4, 2, 8, 2, 2, 4, 4, 6, 2, 4, 2, 4, 4, 2, 2, 4, 4, 4, 2, 2, 2, 2, 8, 4, 2, 4, 2, 4, 4, 2, 6, 2, 6, 4, 2, 4, 4, 8, 2, 4, 2, 4, 4, 2, 8, 2, 2, 4, 2, 2, 2, 4, 4, 4, 4, 4, 4, 6, 4, 2, 2, 2, 4, 4, 4, 4, 4, 8, 2, 2

Offset: 1

Author

Omar E. Pol, Jan 13 2012

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• George E. Andrews, Frank G. Garvan, and Jie Liang, Self-conjugate vector partitions and the parity of the spt-function, Acta Arith., Vol. 158, No. 3 (2013), pp. 199-218; alternative link; author's link.

Crossrefs

Cf. A000005, A001620, A092269, A134517, A183010, A183011, A195052, A195053.

Programs

GAP

List([1..100],n->Tau(24*n-1)); # Muniru A Asiru, Jun 27 2018

Maple

seq(numtheory:-tau(24*n-1),n=1..100); # Robert Israel, Jun 27 2018

Mathematica

Table[DivisorSigma[0, 24*n-1], {n, 100}] (* T. D. Noe, Jan 14 2012 *)

PARI

a(n) = numdiv(24*n-1); \\ Amiram Eldar, Dec 22 2023

Formula

a(n) = A000005(A183010(n)).

a(n) = 2 * A195052(n).

Sum_{k=1..n} a(k) ~ (n/3) * (log(n) + 2*gamma - 1 + 5*log(2) + 2*log(3)), where gamma is Euler's constant (A001620). - Amiram Eldar, Dec 22 2023