A369687 a(n) = Sum_{p|n, p prime} p^phi(n/p).
0, 2, 3, 2, 5, 7, 7, 4, 9, 21, 11, 13, 13, 71, 106, 16, 17, 73, 19, 41, 778, 1035, 23, 97, 625, 4109, 729, 113, 29, 362, 31, 256, 59170, 65553, 18026, 145, 37, 262163, 531610, 881, 41, 4874, 43, 1145, 22186, 4194327, 47, 6817, 117649, 1049201, 43047010, 4265, 53, 262873, 9780266, 6497
Offset: 1
Programs
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Mathematica
Table[DivisorSum[n, #^EulerPhi[n/#] &, PrimeQ[#] &], {n, 60}] -
Python
from sympy import totient, primefactors def A369687(n): return sum(p**totient(n//p) for p in primefactors(n)) # Chai Wah Wu, Jan 28 2024
Formula
a(p^k) = p^((p-1)*p^(k-2)+floor(1/k)/p) for p prime and k>=1. - Wesley Ivan Hurt, Jul 16 2025