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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

Seiichi Manyama, Table of n, a(n) for n = 1..10000

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

Cf. A000005 (tau), A001248, A006881, A347405, A348223.

Sequence in context: A078646 A264405 A304650 * A317581 A035217 A277808

Adjacent sequences:  A347989 A347990 A347991 * A347993 A347994 A347995

KEYWORD

sign

AUTHOR

Seiichi Manyama, Oct 08 2021

STATUS

approved

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Last modified January 21 23:58 EST 2022. Contains 350481 sequences. (Running on oeis4.)