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A328729 Dirichlet g.f.: zeta(s) / (zeta(s-1) * zeta(2*s)). 0
1, -1, -2, -2, -4, 2, -6, 0, -3, 4, -10, 4, -12, 6, 8, 0, -16, 3, -18, 8, 12, 10, -22, 0, -5, 12, 0, 12, -28, -8, -30, 0, 20, 16, 24, 6, -36, 18, 24, 0, -40, -12, -42, 20, 12, 22, -46, 0, -7, 5, 32, 24, -52, 0, 40, 0, 36, 28, -58, -16, -60, 30, 18, 0, 48, -20, -66, 32, 44, -24 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Dirichlet inverse of A206369.

LINKS

Table of n, a(n) for n=1..70.

FORMULA

a(1) = 1; a(n) = -Sum_{d|n, d<n} A206369(n/d) * a(d).

a(n) = Sum_{d|n} mu(n/d)^2 * mu(d) * d.

a(n) = Sum_{d|n} A008966(n/d) * A055615(d).

a(n) = Sum_{d|n} A271102(n/d) * A023900(d).

MATHEMATICA

a[1] = 1; a[n_] := -Sum[(n/d) DivisorSum[n/d, LiouvilleLambda[#]/# &] a[d], {d, Most @ Divisors[n]}]; Table[a[n], {n, 1, 70}]

Table[DivisorSum[n, MoebiusMu[n/#]^2 MoebiusMu[#] # &], {n, 1, 70}]

CROSSREFS

Cf. A008683, A008966, A023900, A046099 (positions of 0's), A046692, A055615, A206369, A271102.

Sequence in context: A290088 A179013 A090397 * A329733 A289624 A258446

Adjacent sequences:  A328726 A328727 A328728 * A328730 A328731 A328732

KEYWORD

sign,mult

AUTHOR

Ilya Gutkovskiy, Oct 26 2019

STATUS

approved

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Last modified September 30 17:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)