A062785 a(n) = Chowla's function of n * sigma(n).

0, 0, 0, 14, 0, 60, 0, 90, 39, 126, 0, 420, 0, 216, 192, 434, 0, 780, 0, 882, 320, 468, 0, 2100, 155, 630, 480, 1512, 0, 2952, 0, 1890, 672, 1026, 576, 4914, 0, 1260, 896, 4410, 0, 5088, 0, 3276, 2496, 1800, 0, 9300, 399, 3906, 1440, 4410, 0, 7800, 1152, 7560, 1760, 2790, 0, 17976, 0, 3168, 4160, 7874, 1512

Offset: 1

Author

Jason Earls, Jul 18 2001

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Crossrefs

Cf. A000203, A048050.

Cf. A002117, A086463.

Programs

Mathematica

a[n_] := Module[{s = DivisorSigma[1, n]}, s*(s - n - 1)]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Apr 01 2024 *)

PARI

a(n) = {my(s = sigma(n)); if(n == 1, 0, s*(s-n-1));}

Formula

a(n) = A000203(n)*A048050(n). - Michel Marcus, Jun 29 2018

Sum_{k=1..n} a(k) ~ (5*zeta(3)/6 - Pi^2/18) * n^3. - Amiram Eldar, Apr 01 2024

Extensions

a(1) corrected by Amiram Eldar, Apr 01 2024