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A309324 Expansion of Sum_{k>=1} psi(k) * x^k/(1 + x^k), where psi = Dedekind psi function (A001615). 0
1, 2, 5, 2, 7, 10, 9, 2, 17, 14, 13, 10, 15, 18, 35, 2, 19, 34, 21, 14, 45, 26, 25, 10, 37, 30, 53, 18, 31, 70, 33, 2, 65, 38, 63, 34, 39, 42, 75, 14, 43, 90, 45, 26, 119, 50, 49, 10, 65, 74, 95, 30, 55, 106, 91, 18, 105, 62, 61, 70, 63, 66, 153, 2, 105, 130, 69, 38, 125, 126, 73 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Dirichlet convolution of sum of odd divisors function with characteristic function of squarefree numbers.

LINKS

Table of n, a(n) for n=1..71.

FORMULA

a(n) = Sum_{d|n} (-1)^(n/d+1) * psi(d).

a(n) = Sum_{d|n} mu(n/d)^2 * A000593(d).

MATHEMATICA

nmax = 71; CoefficientList[Series[Sum[DirichletConvolve[j, MoebiusMu[j]^2, j, k]  x^k/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Table[Sum[MoebiusMu[n/d]^2 Plus @@ Select[Divisors@ d, OddQ], {d, Divisors[n]}], {n, 1, 71}]

CROSSREFS

Cf. A000593, A001615, A008966, A060648, A193356.

Sequence in context: A246341 A246355 A016580 * A220072 A065223 A248154

Adjacent sequences:  A309321 A309322 A309323 * A309325 A309326 A309327

KEYWORD

nonn,mult

AUTHOR

Ilya Gutkovskiy, Jul 23 2019

STATUS

approved

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Last modified December 5 21:00 EST 2019. Contains 329779 sequences. (Running on oeis4.)