A369739 a(n) = Sum_{p|n, p prime} p^tau(n/p).
0, 2, 3, 4, 5, 13, 7, 8, 9, 29, 11, 43, 13, 53, 34, 16, 17, 89, 19, 141, 58, 125, 23, 145, 25, 173, 27, 359, 29, 722, 31, 32, 130, 293, 74, 793, 37, 365, 178, 689, 41, 2498, 43, 1347, 206, 533, 47, 499, 49, 633, 298, 2213, 53, 745, 146, 2465, 370, 845, 59, 16610, 61, 965, 424, 64, 194
Offset: 1
Programs
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Mathematica
Table[DivisorSum[n, #^DivisorSigma[0, n/#] &, PrimeQ[#] &], {n, 60}]
Formula
a(p^k) = p^k, for p prime and k >= 1. - Wesley Ivan Hurt, Jun 26 2024