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A130054 Inverse Moebius transform of A023900. 3
1, 0, -1, -1, -3, 0, -5, -2, -3, 0, -9, 1, -11, 0, 3, -3, -15, 0, -17, 3, 5, 0, -21, 2, -7, 0, -5, 5, -27, 0, -29, -4, 9, 0, 15, 3, -35, 0, 11, 6, -39, 0, -41, 9, 9, 0, -45, 3, -11, 0, 15, 11, -51, 0, 27, 10, 17, 0, -57, -3, -59, 0, 15, -5, 33, 0, -65, 15, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

A126988 * A130054 = d(n), A000005: (1, 2, 2, 3, 2, 4, 2, 4, 3, 4,...).

Multiplicative because A023900 is. - Andrew Howroyd, Aug 03 2018

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = sumdiv(n, d, A023900(n/d)). - Andrew Howroyd, Aug 03 2018

a(n) = Sum_{d|n} d*mu(d)*tau(n/d). - Ridouane Oudra, Nov 17 2019

MAPLE

with(numtheory): seq(add(d*mobius(d)*tau(n/d), d in divisors(n)), n=1..60); # Ridouane Oudra, Nov 17 2019

MATHEMATICA

b[n_] := Sum[d MoebiusMu[d], {d, Divisors[n]}];

a[n_] := Sum[b[n/d], {d, Divisors[n]}];

a /@ Range[1, 100] (* Jean-Fran├žois Alcover, Sep 20 2019, from PARI *)

PROG

(PARI) \\ here b(n) is A023900

b(n)={sumdivmult(n, d, d*moebius(d))}

a(n)={sumdiv(n, d, b(n/d))} \\ Andrew Howroyd, Aug 03 2018

(MAGMA) [&+[d*MoebiusMu(d)*NumberOfDivisors(n div d):d in Divisors(n)]:n in [1..70]]; // Marius A. Burtea, Nov 17 2019

CROSSREFS

Row sums of A129691.

Cf. A126988, A000005, A023900.

Sequence in context: A304027 A187886 A324103 * A236146 A196111 A261628

Adjacent sequences:  A130051 A130052 A130053 * A130055 A130056 A130057

KEYWORD

sign,mult

AUTHOR

Gary W. Adamson, May 04 2007

EXTENSIONS

Name changed and terms a(11) and beyond from Andrew Howroyd, Aug 03 2018

STATUS

approved

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Last modified January 28 22:40 EST 2020. Contains 331328 sequences. (Running on oeis4.)