A347398 Expansion of g.f. Sum_{k>=1} k^k * x^(k^k)/(1 - x^(k^k)).

1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 28, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 28, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 28, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 32, 1, 1, 1, 5

Offset: 1

Author

Seiichi Manyama, Aug 30 2021

Keywords

• nonn

Examples

			1^1 | 108, 2^2 | 108 and 3^3 | 108. So a(108) = 1^1 + 2^2 + 3^3 = 32.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A000312, A035316, A113061, A300909, A347397, A347399.

Programs

PARI

a(n) = sum(k=1, n, (n%k^k==0)*k^k);

Formula

a(n) = A347397(n) - A347397(n-1) for n > 1.

a(n) = Sum_{k=1..n, k^k | n} k^k.