A369903 a(n) = Sum_{p|n, p prime} n^sigma(n/p).
0, 2, 3, 64, 5, 1512, 7, 2097152, 6561, 1001000, 11, 8916136280064, 13, 1475791800, 11441250, 1152921504606846976, 17, 21979796247097344, 19, 262144000000001280000000, 37823053842, 12855002631059864, 23, 442501521100279866178075737690262732800, 244140625
Offset: 1
Programs
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Mathematica
Table[DivisorSum[n, n^DivisorSigma[1, n/#] &, PrimeQ[#] &], {n, 30}]
Formula
a(p^k) = p^(k*(1-p^k)/(1-p)), for prime p and k >= 1. - Wesley Ivan Hurt, Jun 26 2024