A283123 a(n) = sigma(9*n).

13, 39, 40, 91, 78, 120, 104, 195, 121, 234, 156, 280, 182, 312, 240, 403, 234, 363, 260, 546, 320, 468, 312, 600, 403, 546, 364, 728, 390, 720, 416, 819, 480, 702, 624, 847, 494, 780, 560, 1170, 546, 960, 572, 1092, 726, 936, 624, 1240, 741, 1209

Offset: 1

Author

Seiichi Manyama, Mar 01 2017

Keywords

• nonn

Comments

In general, for k>=1, Sum_{j=1..n} sigma(j*k) ~ A069097(k) * Pi^2 * n^2 / (12*k). - Vaclav Kotesovec, May 11 2024

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Sigma(k*n): A000203 (k=1), A062731 (k=2), A144613 (k=3), A193553 (k=4), A283118 (k=5), A224613 (k=6), A283078 (k=7), A283122 (k=8), this sequence (k=9).

Cf. A008591.

Programs

Mathematica

Table[DivisorSigma[1, 9 n], {n, 50}] (* Michael De Vlieger, Mar 01 2017 *)

PARI

a(n) = sigma(9*n) \\ Amiram Eldar, Dec 16 2022

Formula

a(n) = A000203(9*n).

Sum_{k=1..n} a(k) = (35*Pi^2/36) * n^2 + O(n*log(n)). - Amiram Eldar, Dec 16 2022