A195052 Number of divisors of 24*n - 1 divided by 2.

1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 4, 1, 1, 2, 2, 3, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 4, 2, 1, 2, 1, 2, 2, 1, 3, 1, 3, 2, 1, 2, 2, 4, 1, 2, 1, 2, 2, 1, 4, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 2, 1, 1, 1, 2, 2, 2, 2, 2, 4, 1, 1

Offset: 1

Author

Omar E. Pol, Jan 13 2012

Keywords

• nonn
• easy

Comments

It appears that this sequence has the same parity as the spt function A092269 (See A195053). - Omar E. Pol, Jan 30 2012

Links

• 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, A195051, A195053.

Programs

Mathematica

a[n_] := DivisorSigma[0, 24*n-1]/2; Array[a, 100] (* Amiram Eldar, Dec 22 2023 *)

PARI

a(n) = numdiv(24*n-1)/2; \\ Amiram Eldar, Dec 22 2023

Formula

a(n) = A000005(A183010(n))/2 = A195051(n)/2.

Sum_{k=1..n} a(k) ~ (n/6) * (log(n) + 2*gamma - 1 + 5*log(2) + 2*log(3)), where gamma is Euler's constant (A001620). - Amiram Eldar, Dec 22 2023