A369868 a(n) = Sum_{p|n, p prime} n^pi(n/p).

0, 1, 1, 4, 1, 42, 1, 64, 81, 1010, 1, 1872, 1, 38430, 3600, 65536, 1, 110808, 1, 160400, 194922, 5153654, 1, 8294400, 15625, 308915802, 531441, 481891088, 1, 729837000, 1, 1073741824, 39136482, 52523350178, 1543500, 78424630272, 1, 4347792138534, 3518745282

Offset: 1

Author

Wesley Ivan Hurt, Feb 03 2024

Keywords

• nonn
• easy

Crossrefs

Cf. A000720 (pi), A345301, A369745, A369747.

Programs

Mathematica

Table[DivisorSum[n, n^PrimePi[n/#] &, PrimeQ[#] &], {n, 60}]

Formula

a(p^k) = p^(k*pi(p^(k-1))), for p prime and k >= 1. - Wesley Ivan Hurt, Jun 26 2024