A369893 a(n) = Sum_{p|n, p prime} n^tau(n/p).
0, 2, 3, 16, 5, 72, 7, 512, 81, 200, 11, 22464, 13, 392, 450, 65536, 17, 110808, 19, 168000, 882, 968, 23, 191434752, 625, 1352, 19683, 636608, 29, 2430000, 31, 33554432, 2178, 2312, 2450, 4353564672, 37, 2888, 3042, 4098560000, 41, 9335088, 43, 3833280
Offset: 1
Programs
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Mathematica
Table[DivisorSum[n, n^DivisorSigma[0, n/#] &, PrimeQ[#] &], {n, 60}]
Formula
a(p^k) = p^(k^2), for prime p and k >= 1. - Wesley Ivan Hurt, Jun 26 2024