A307653 a(n) = Sum_{d|n} mu(d) * d^d.

1, -3, -26, -3, -3124, 46626, -823542, -3, -26, 9999996872, -285311670610, 46626, -302875106592252, 11112006824734470, 437893890380856224, -3, -827240261886336764176, 46626, -1978419655660313589123978, 9999996872, 5842587018385982521380300852

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..388

Formula

a(prime(n)^m) = 1 - prime(n)^prime(n) = -A088730(n) for m > 0.

G.f.: Sum_{k>=1} mu(k)*k^k*x^k/(1 - x^k). - Ilya Gutkovskiy, Apr 20 2019

Example

a(6) = 1 - 2^2 - 3^3 + 6^6 = 46626.

Mathematica

Array[DivisorSum[#, MoebiusMu[#]*#^# &] &, 21] (* Michael De Vlieger, Apr 21 2019 *)

Prog

(PARI) {a(n) = sumdiv(n, d, moebius(d)*d^d)}

Crossrefs

Cf. A000040, A008683, A023900, A088730, A307654, A321222.

Sequence in context: A144788 A182135 A307654 * A326610 A221616 A321222

Adjacent sequences: A307650 A307651 A307652 * A307654 A307655 A307656

Keyword

sign

Author

Seiichi Manyama, Apr 20 2019

Status

approved