OFFSET
1,3
FORMULA
a(n) = Sum_{d|n} A002129(d).
a(n) = Sum_{d|n} (-1)^(d + 1) * d * tau(n/d).
MATHEMATICA
nmax = 65; CoefficientList[Series[Sum[DivisorSigma[0, k] x^k/(1 + x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
a[n_] := Sum[(-1)^(d + 1) d DivisorSigma[0, n/d], {d, Divisors[n]}]; Table[a[n], {n, 1, 65}]
PROG
(PARI) a(n) = {sumdiv(n, d, (-1)^(d + 1) * d * numdiv(n/d))} \\ Andrew Howroyd, Sep 14 2019
(Magma) [&+[(-1)^(d+1)*d*#Divisors(n div d):d in Divisors(n)]:n in [1..65]]; // Marius A. Burtea, Sep 14 2019
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Ilya Gutkovskiy, Sep 14 2019
STATUS
approved