A369905 a(n) = Sum_{p|n, p prime} n^omega(n/p).
0, 1, 1, 4, 1, 12, 1, 8, 9, 20, 1, 156, 1, 28, 30, 16, 1, 342, 1, 420, 42, 44, 1, 600, 25, 52, 27, 812, 1, 2700, 1, 32, 66, 68, 70, 2592, 1, 76, 78, 1640, 1, 5292, 1, 1980, 2070, 92, 1, 2352, 49, 2550, 102, 2756, 1, 2970, 110, 3192, 114, 116, 1, 223200, 1, 124, 4032
Offset: 1
Programs
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Mathematica
Table[DivisorSum[n, n^PrimeNu[n/#] &, PrimeQ[#] &], {n, 100}]
Formula
a(p^k) = 1 for p prime and k = 1, else p^k if k >= 2. - Wesley Ivan Hurt, Jun 26 2024