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A347992 a(n) = Sum_{d|n} (-1)^(tau(d) - 1). 4
1, 0, 0, 1, 0, -2, 0, 0, 1, -2, 0, -2, 0, -2, -2, 1, 0, -2, 0, -2, -2, -2, 0, -4, 1, -2, 0, -2, 0, -6, 0, 0, -2, -2, -2, -1, 0, -2, -2, -4, 0, -6, 0, -2, -2, -2, 0, -4, 1, -2, -2, -2, 0, -4, -2, -4, -2, -2, 0, -8, 0, -2, -2, 1, -2, -6, 0, -2, -2, -6, 0, -4, 0, -2, -2, -2, -2, -6, 0, -4, 1, -2, 0, -8, -2, -2, -2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
LINKS
FORMULA
If p is prime, a(p) = 0.
If p is prime, a(p^even) = 1 and a(p^odd) = 0. - Michel Marcus, Oct 13 2021
If p <> q primes, a(p*q) = -2 (A006881). - Bernard Schott, Oct 13 2021
G.f.: Sum_{k>=1} (-1)^(tau(k) - 1) * x^k/(1 - x^k). - Seiichi Manyama, Oct 14 2021
MATHEMATICA
a[n_] := DivisorSum[n, (-1)^(DivisorSigma[0, #] - 1) &]; Array[a, 100] (* Amiram Eldar, Oct 08 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, (-1)^(numdiv(d)-1));
(PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, (-1)^(numdiv(k)-1)*x^k/(1-x^k)))
CROSSREFS
Sequence in context: A264405 A304650 A360670 * A317581 A359865 A035217
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 08 2021
STATUS
approved

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Last modified May 21 08:24 EDT 2024. Contains 372729 sequences. (Running on oeis4.)