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A318768 a(n) = Sum_{d|n} (-1)^(n/d+1) * Sum_{j|d} tau(j), where tau = number of divisors (A000005). 3
1, 2, 4, 2, 4, 8, 4, 0, 10, 8, 4, 8, 4, 8, 16, -5, 4, 20, 4, 8, 16, 8, 4, 0, 10, 8, 20, 8, 4, 32, 4, -14, 16, 8, 16, 20, 4, 8, 16, 0, 4, 32, 4, 8, 40, 8, 4, -20, 10, 20, 16, 8, 4, 40, 16, 0, 16, 8, 4, 32, 4, 8, 40, -28, 16, 32, 4, 8, 16, 32, 4, 0, 4, 8, 40, 8, 16, 32, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

G.f.: Sum_{k>=1} tau_3(k)*x^k/(1 + x^k), where tau_3() = A007425.

L.g.f.: log(Product_{k>=1} (1 + x^k)^(tau_3(k)/k)) = Sum_{n>=1} a(n)*x^n/n.

MATHEMATICA

Table[Sum[(-1)^(n/d + 1) Sum[DivisorSigma[0, j], {j, Divisors[d]}], {d, Divisors[n]}], {n, 79}]

nmax = 79; Rest[CoefficientList[Series[Sum[DivisorSum[k, DivisorSigma[0, #] &] x^k/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]]

nmax = 79; Rest[CoefficientList[Series[Log[Product[(1 + x^k)^(DivisorSum[k, DivisorSigma[0, #] &]/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]]

PROG

(PARI) a(n) = sumdiv(n, d, (-1)^(n/d+1) * sumdiv(d, j, numdiv(j))); \\ Michel Marcus, Sep 04 2018

CROSSREFS

Cf. A000005, A007425, A007426, A051062 (positions of 0's), A288571.

Sequence in context: A227346 A296141 A286536 * A166242 A143107 A051638

Adjacent sequences:  A318765 A318766 A318767 * A318769 A318770 A318771

KEYWORD

sign,mult

AUTHOR

Ilya Gutkovskiy, Sep 03 2018

STATUS

approved

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Last modified April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)