%I #10 May 09 2022 02:44:16

%S 0,1,195,3496,38195,192780,977386,3216320,9860049,27321870,65803045,

%T 144005856,308944925,635774072,1112550390,2153146880,3618341556,

%U 6391671525,9949570455,16725562160,24691972080,40979569092,56807498030,89450231040,120404165825

%N a(n) = Sum(k^6*sigma(k)*sigma(n-k),k=1..n-1).

%C This was formerly A001479.

%H Colin Barker, <a href="/A259694/b259694.txt">Table of n, a(n) for n = 1..1000</a>

%H J. Touchard, <a href="/A000385/a000385.pdf">On prime numbers and perfect numbers</a>, Scripta Math., 129 (1953), 35-39. [Annotated scanned copy]

%p 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(6);

%o (PARI) a(n) = sum(k=1, n-1, k^6*sigma(k)*sigma(n-k)) \\ _Colin Barker_, Jul 16 2015

%Y Cf. A000385, A000441, A000477, A000499, A259692, A259693, A259695, A259696.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Jul 03 2015