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A317673

Moebius transform of A129502.

1, 2, -1, 3, -1, -2, -1, 4, 0, -2, -1, -3, -1, -2, 1, 5, -1, 0, -1, -3, 1, -2, -1, -4, 0, -2, 0, -3, -1, 2, -1, 6, 1, -2, 1, 0, -1, -2, 1, -4, -1, 2, -1, -3, 0, -2, -1, -5, 0, 0, 1, -3, -1, 0, 1, -4, 1, -2, -1, 3, -1, -2, 0, 7, 1, 2, -1, -3, 1, 2, -1, 0, -1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Dirichlet convolution of A209635 and A209229.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1024

FORMULA

Multiplicative with a(2^e) = e+1, and if p is an odd prime, a(p) = -1 and a(p^e) = 0 for e >= 2. - Amiram Eldar, Aug 28 2023

MATHEMATICA

a[n_] := Module[{e}, Sum[e = IntegerExponent[d, 2]; If[d == 2^e, MoebiusMu[n/d] Binomial[2 + e, 2], 0], {d, Divisors[n]}]];

a /@ Range[1, 100] (* Jean-François Alcover, Sep 24 2019, from PARI *)