A359812 a(n) = Sum_{d|n} (-1)^(d-1) * d^(n/d-1).

1, 0, 2, -2, 2, -1, 2, -12, 11, -11, 2, -27, 2, -57, 108, -200, 2, -40, 2, -653, 780, -1013, 2, -1177, 627, -4083, 6644, -11959, 2, 5043, 2, -49680, 59172, -65519, 18028, -26670, 2, -262125, 531612, -713423, 2, 515723, 2, -3144419, 5180382, -4194281, 2

Offset

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Formula

G.f.: -Sum_{k>0} (-x)^k / (1 - k * x^k).

If p is an odd prime, a(p) = 2.

Mathematica

a[n_] := DivisorSum[n, (-1)^(#-1) * #^(n/# - 1) &]; Array[a, 50] (* Amiram Eldar, Aug 09 2023 *)

Prog

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

Crossrefs

Cf. A087909, A359811.

Sequence in context: A124369 A205013 A138258 * A308367 A205599 A327891

Adjacent sequences: A359809 A359810 A359811 * A359813 A359814 A359815

Keyword

sign,easy

Author

Seiichi Manyama, Jan 14 2023

Status

approved