A092345 a(0)=1; a(n) = sigma_1(n) + sigma_3(n).

1, 2, 12, 32, 80, 132, 264, 352, 600, 770, 1152, 1344, 2072, 2212, 3120, 3552, 4712, 4932, 6852, 6880, 9240, 9664, 12024, 12192, 16440, 15782, 19824, 20480, 25168, 24420, 31824, 29824, 37512, 37344, 44280, 43392, 55352, 50692, 61800, 61600, 73800, 68964, 86784

Offset: 0

Author

N. J. A. Sloane, Mar 20 2004

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000203, A001158.

Programs

Mathematica

nxt[{n_,a_}]:={n+1,DivisorSigma[1,n+1]+DivisorSigma[3,n+1]}; NestList[nxt,{0,1},50][[All,2]] (* Harvey P. Dale, Apr 14 2021 *)

PARI

a(n) = if(n == 0, 1, my(f = factor(n)); sigma(f, 1) + sigma(f, 3)); \\ Amiram Eldar, Jan 03 2025

Formula

G.f.: 1 + Sum_{k>=1} k*(k^2 + 1)*x^k/(1 - x^k). - Ilya Gutkovskiy, Mar 17 2017