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

1,4

Comments

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

Links

Table of n, a(n) for n=1..86.

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.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A001620, A092269, A134517, A183010, A183011, A195051, A195053.

Sequence in context: A213366 A212648 A255507 * A104637 A188795 A325444

Adjacent sequences: A195049 A195050 A195051 * A195053 A195054 A195055

Keyword

nonn,easy

Author

Omar E. Pol, Jan 13 2012

Status

approved