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

1,2

Links

Table of n, a(n) for n=1..34.

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

Mathematica

Table[DivisorSum[n, n^EulerPhi[n/#] &, PrimeQ[#] &], {n, 40}]

Crossrefs

Cf. A000010, A345893, A347104, A369687, A369779.

Sequence in context: A153719 A024637 A037328 * A028427 A037329 A344848

Adjacent sequences: A369779 A369780 A369781 * A369783 A369784 A369785

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 31 2024

Status

approved