A345265 a(n) = Sum_{d|n} n^rad(d).

1, 6, 30, 36, 3130, 46914, 823550, 200, 1467, 10000100110, 285311670622, 5973996, 302875106592266, 11112006930971730, 437893890381622140, 1040, 827240261886336764194, 68036454, 1978419655660313589123998, 20480003200820, 5842587018385982523182222244, 341427877364220141714948135418

Offset: 1

Author

Wesley Ivan Hurt, Jun 12 2021

Keywords

• nonn

Examples

			a(8) = Sum_{d|8} 8^rad(d) = 8^1 + 8^2 + 8^2 + 8^2 = 200.
		

Crossrefs

Cf. A007947 (rad), A101340.

Programs

Mathematica

Table[Sum[(1 - Ceiling[n/i] + Floor[n/i]) n^Product[k^((PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[i/k] + Floor[i/k])), {k, i}], {i, n}], {n, 30}]

PARI

rad(n) = factorback(factorint(n)[, 1]);
a(n) = sumdiv(n, d, n^rad(d)); \\ Michel Marcus, Jun 12 2021

Formula

a(p) = Sum_{d|p} p^rad(d) = p^1 + p^p = p^p + p, for p prime.