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A359812
a(n) = Sum_{d|n} (-1)^(d-1) * d^(n/d-1).
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
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
Sequence in context: A124369 A205013 A138258 * A308367 A205599 A327891
KEYWORD
sign,easy
AUTHOR
Seiichi Manyama, Jan 14 2023
STATUS
approved