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%I #7 May 21 2021 04:17:38
%S 1,11,85,1103,15631,284795,5764809,134745175,3486961642,100097682141,
%T 3138428376733,107019534806039,3937376385699303,155577590686826319,
%U 6568408813691811835,295152408847835466855,14063084452067724991027,708238048886862707907062,37589973457545958193355621,2097154000001929438984022793
%N a(n) = Sum_{d|n} d * sigma_d(d), where sigma_k(n) is the sum of the k-th powers of the divisors of n.
%C If p is prime, a(p) = Sum_{d|p} d * sigma_d(d) = 1*(1^1) + p*(1^p + p^p) = 1 + p + p^(p+1).
%e a(6) = Sum_{d|6} d * sigma_d(d) = 1*(1^1) + 2*(1^2 + 2^2) + 3*(1^3 + 3^3) + 6*(1^6 + 2^6 + 3^6 + 6^6) = 284795.
%t Table[Sum[k*DivisorSigma[k, k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 30}]
%o (PARI) a(n) = sumdiv(n, d, d*sigma(d, d)); \\ _Michel Marcus_, May 21 2021
%Y Cf. A245466, A321141, A334874, A343781, A344434.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, May 20 2021
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