A369740 a(n) = Sum_{p|n, p prime} p^sigma(n/p).
0, 2, 3, 8, 5, 43, 7, 128, 81, 189, 11, 6283, 13, 599, 1354, 32768, 17, 539633, 19, 340269, 8962, 5427, 23, 282784363, 15625, 18581, 1594323, 17600759, 29, 648338330, 31, 2147483648, 546082, 267057, 508274, 23426548268849, 37, 1055435, 4811530, 4428564089229, 41, 300565790978
Offset: 1
Programs
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Mathematica
Table[DivisorSum[n, #^DivisorSigma[1, n/#] &, PrimeQ[#] &], {n, 50}]
Formula
a(p^k) = p^((1-p^k)/(1-p)) for p prime and k>=1. - Wesley Ivan Hurt, Jul 16 2025