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%I #7 Jun 26 2024 15:07:19
%S 0,2,3,16,5,72,7,512,81,200,11,22464,13,392,450,65536,17,110808,19,
%T 168000,882,968,23,191434752,625,1352,19683,636608,29,2430000,31,
%U 33554432,2178,2312,2450,4353564672,37,2888,3042,4098560000,41,9335088,43,3833280
%N a(n) = Sum_{p|n, p prime} n^tau(n/p).
%F a(p^k) = p^(k^2), for prime p and k >= 1. - _Wesley Ivan Hurt_, Jun 26 2024
%t Table[DivisorSum[n, n^DivisorSigma[0, n/#] &, PrimeQ[#] &], {n, 60}]
%Y Cf. A000005 (tau), A062799, A319131.
%K nonn,easy
%O 1,2
%A _Wesley Ivan Hurt_, Feb 04 2024