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%I #14 May 09 2022 02:44:57
%S 0,1,387,9904,142475,850500,5287786,19400960,68736681,210682950,
%T 565317445,1328193216,3163440917,6945663368,13045807350,26914795520,
%U 48673795956,89900901837,149363037975,262436871200,409003474320,711715515852,1035199173422,1683466675200
%N a(n) = Sum_{k=1..n-1} k^7 * sigma(k) * sigma(n-k).
%C This was formerly A001480.
%H Colin Barker, <a href="/A259695/b259695.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(7);
%t Table[Sum[k^7 DivisorSigma[1,k]DivisorSigma[1,n-k],{k,n-1}],{n,30}] (* _Harvey P. Dale_, Dec 14 2015 *)
%o (PARI) a(n) = sum(k=1, n-1, k^7*sigma(k)*sigma(n-k)) \\ _Colin Barker_, Jul 16 2015
%Y Cf. A000203, A000385, A000441, A000477, A000499, A259692, A259693, A259694, A259696.
%K nonn
%O 1,3
%A _N. J. A. Sloane_, Jul 03 2015
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