A369782 a(n) = Sum_{p|n, p prime} n^phi(n/p).
0, 2, 3, 4, 5, 42, 7, 64, 81, 10010, 11, 288, 13, 7529550, 50850, 65536, 17, 34012548, 19, 160400, 85766562, 26559922791446, 23, 663552, 390625, 95428956661682202, 387420489, 481891088, 29, 656100810900, 31, 1099511627776, 1531578985265538, 3189059870763703892770850
Offset: 1
Programs
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Mathematica
Table[DivisorSum[n, n^EulerPhi[n/#] &, PrimeQ[#] &], {n, 40}]
Formula
a(p^k) = p^(k*(p-1)*p^(k-2)+floor(1/k)/p) for p prime and k>=1. - Wesley Ivan Hurt, Jul 16 2025