A345263 a(n) = Sum_{d|n} d^rad(d).

1, 5, 28, 21, 3126, 46688, 823544, 85, 757, 10000003130, 285311670612, 3032688, 302875106592254, 11112006826381564, 437893890380862528, 341, 827240261886336764178, 34059641, 1978419655660313589123980, 10250000003146, 5842587018385982521381947992, 341427877364219557681958394200

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..22.

Formula

a(prime(n)) = A125137(n). - Michel Marcus, Jun 12 2021

Example

a(4) = Sum_{d|4} d^rad(d) = 1^1 + 2^2 + 4^2 = 21.
a(6) = Sum_{d|6} d^rad(d) = 1^1 + 2^2 + 3^3 + 6^6 = 46688.

Mathematica

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

Prog

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

Crossrefs

Cf. A007947 (rad), A125137.

Sequence in context: A321236 A351774 A344579 * A218346 A106679 A341061

Adjacent sequences: A345260 A345261 A345262 * A345264 A345265 A345266

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 12 2021

Status

approved