A259695 a(n) = Sum_{k=1..n-1} k^7 * sigma(k) * sigma(n-k).

0, 1, 387, 9904, 142475, 850500, 5287786, 19400960, 68736681, 210682950, 565317445, 1328193216, 3163440917, 6945663368, 13045807350, 26914795520, 48673795956, 89900901837, 149363037975, 262436871200, 409003474320, 711715515852, 1035199173422, 1683466675200

Offset: 1

Author

N. J. A. Sloane, Jul 03 2015

Keywords

• nonn

Comments

This was formerly A001480.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• J. Touchard, On prime numbers and perfect numbers, Scripta Math., 129 (1953), 35-39. [Annotated scanned copy]

Crossrefs

Cf. A000203, A000385, A000441, A000477, A000499, A259692, A259693, A259694, A259696.

Programs

Maple

S:=(n,e)->add(k^e*sigma(k)*sigma(n-k),k=1..n-1); f:=e->[seq(S(n,e),n=1..30)]; f(7);

Mathematica

Table[Sum[k^7 DivisorSigma[1,k]DivisorSigma[1,n-k],{k,n-1}],{n,30}] (* Harvey P. Dale, Dec 14 2015 *)

PARI

a(n) = sum(k=1, n-1, k^7*sigma(k)*sigma(n-k)) \\ Colin Barker, Jul 16 2015