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A317673 Moebius transform of A129502. 3
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

LINKS

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

FORMULA

Dirichlet convolution of A209635 and A209229.

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-Fran├žois Alcover, Sep 24 2019, from PARI *)

PROG

(PARI) a(n)={sumdiv(n, d,  my(e=valuation(d, 2)); if(d==1<<e, moebius(n/d) * binomial(2+e, 2), 0))}

CROSSREFS

First column of A129501.

Cf. A129502, A209229, A209635 (Moebius transform of A104117).

Sequence in context: A157226 A156249 A187808 * A317954 A164677 A001511

Adjacent sequences:  A317670 A317671 A317672 * A317674 A317675 A317676

KEYWORD

sign,mult

AUTHOR

Andrew Howroyd, Aug 03 2018

STATUS

approved

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Last modified May 31 19:11 EDT 2020. Contains 334748 sequences. (Running on oeis4.)