A359188 a(n) = Sum_{d|n} mu(n/d) * d * (n/d)^(d-1), where mu() is the Moebius function (A008683).

1, 1, 2, 0, 4, -11, 6, -24, -18, -79, 10, -276, 12, -447, -464, -1008, 16, -3636, 18, -5580, -5228, -11263, 22, -41184, -3100, -53247, -59022, -116004, 28, -454501, 30, -524256, -649868, -1114111, -121344, -4438368, 36, -4980735, -6909200, -11106720, 40, -44114197, 42

Offset

1,3

Links

Table of n, a(n) for n=1..43.

Formula

G.f.: Sum_{k>=1} mu(k) * x^k/(1 - k * x^k)^2.

If p is prime, a(p) = p - 1.

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[n/#] * # * (n/#)^(#-1) &]; Array[a, 45] (* Amiram Eldar, Aug 27 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, moebius(n/d)*d*(n/d)^(d-1));
(PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, moebius(k)*x^k/(1-k*x^k)^2))

Crossrefs

Cf. A000010, A008683, A167531, A359103.

Sequence in context: A224822 A246928 A167341 * A361269 A343472 A214199

Adjacent sequences: A359185 A359186 A359187 * A359189 A359190 A359191

Keyword

sign

Author

Seiichi Manyama, Dec 19 2022

Status

approved