A374915 a(n) = (n - 1) * (n - 2) * sigma(n).

0, 0, 8, 42, 72, 240, 240, 630, 728, 1296, 1080, 3080, 1848, 3744, 4368, 6510, 4320, 10608, 6120, 14364, 12160, 15120, 11088, 30360, 17112, 25200, 26000, 39312, 22680, 58464, 27840, 58590, 47616, 57024, 53856, 108290, 47880, 79920, 78736, 133380, 65520, 157440

Offset: 1

Author

Seiichi Manyama, Jul 23 2024

Keywords

• nonn

Links

• William Craig, Jan-Willem van Ittersum, and Ken Ono, Integer partitions detect the primes, arXiv:2405.06451v2 [math.CO], Jul 10 2024.

Crossrefs

Cf. A000203, A002127, A002378, A060043, A078837.

Programs

Mathematica

a[n_]:= (n - 1) * (n - 2) * DivisorSigma[1,n]; Array[a,42] (* Stefano Spezia, Jul 23 2024 *)

PARI

a(n) = (n-1)*(n-2)*sigma(n);

Formula

a(n) = A002378(n-2) * A000203(n).

a(n) >= 8 * A002127(n) and the equal sign only holds if n is 1 or prime.