A091986 a(0)=1, a(n) = sigma_3(2n).

1, 9, 73, 252, 585, 1134, 2044, 3096, 4681, 6813, 9198, 11988, 16380, 19782, 25112, 31752, 37449, 44226, 55261, 61740, 73710, 86688, 97236, 109512, 131068, 141759, 160454, 183960, 201240, 219510, 257544, 268128, 299593, 335664, 358722, 390096, 442845

Offset: 0

Author

N. J. A. Sloane, Mar 20 2004

Keywords

• nonn
• easy

Crossrefs

Bisection of A001158.

Cf. A013662, A045823.

Programs

Mathematica

Join[{1},Table[DivisorSigma[3,n],{n,2,80,2}]]  (* Harvey P. Dale, Feb 26 2011 *)

PARI

a(n) = if(n < 1, 1, sigma(2*n, 3)); \\ Amiram Eldar, Dec 12 2023

Formula

Sum_{k=1..n} a(k) ~ (17*zeta(4)/8) * n^4. - Amiram Eldar, Dec 12 2023

G.f.: 1 + Sum_{k>=1} k^3*x^(lcm(k, 2)/2)/(1 - x^(lcm(k, 2)/2)). - Miles Wilson, Jul 10 2025