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A327278 a(n) = Sum_{d|n, d odd} d * mu(d) * mu(n/d). 3
1, -1, -4, 0, -6, 4, -8, 0, 3, 6, -12, 0, -14, 8, 24, 0, -18, -3, -20, 0, 32, 12, -24, 0, 5, 14, 0, 0, -30, -24, -32, 0, 48, 18, 48, 0, -38, 20, 56, 0, -42, -32, -44, 0, -18, 24, -48, 0, 7, -5, 72, 0, -54, 0, 72, 0, 80, 30, -60, 0, -62, 32, -24, 0, 84, -48, -68, 0, 96 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Dirichlet inverse of A000593.

LINKS

Table of n, a(n) for n=1..69.

FORMULA

G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} A000593(k) * A(x^k).

Dirichlet g.f.: 1 / (zeta(s) * zeta(s-1) * (1 - 2^(1-s))).

a(1) = 1; a(n) = -Sum_{d|n, d<n} A000593(n/d) * a(d).

a(n) = Sum_{d|n} A067856(n/d) * A055615(d).

MATHEMATICA

Table[DivisorSum[n, # MoebiusMu[#] MoebiusMu[n/#] &, OddQ[#] &], {n, 1, 69}]

a[n_] := If[n == 1, n, -Sum[If[d < n, DivisorSum[n/d, Mod[#, 2] # &] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 69}]

PROG

[&+[d*MoebiusMu(d)*MoebiusMu(n div d): d in [a:a in Divisors(n)| IsOdd(a)]]:n in [1..70]]; // Marius A. Burtea, Sep 15 2019

CROSSREFS

Cf. A000593, A008683, A046692, A055615, A067856, A206787, A327276.

Sequence in context: A279433 A096272 A021715 * A278210 A291540 A075443

Adjacent sequences:  A327275 A327276 A327277 * A327279 A327280 A327281

KEYWORD

sign,mult

AUTHOR

Ilya Gutkovskiy, Sep 15 2019

STATUS

approved

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Last modified January 21 13:55 EST 2020. Contains 331113 sequences. (Running on oeis4.)