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A327122 Expansion of Sum_{k>=1} sigma(k) * x^k / (1 + x^(2*k)), where sigma = A000203. 1
1, 3, 3, 7, 7, 9, 7, 15, 10, 21, 11, 21, 15, 21, 21, 31, 19, 30, 19, 49, 21, 33, 23, 45, 38, 45, 30, 49, 31, 63, 31, 63, 33, 57, 49, 70, 39, 57, 45, 105, 43, 63, 43, 77, 70, 69, 47, 93, 50, 114, 57, 105, 55, 90, 77, 105, 57, 93, 59, 147, 63, 93, 70, 127, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Inverse Moebius transform of A050469.

LINKS

Table of n, a(n) for n=1..65.

FORMULA

a(n) = Sum_{d|n} A050469(d).

MATHEMATICA

nmax = 65; CoefficientList[Series[Sum[DivisorSigma[1, k] x^k/(1 + x^(2 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

A050469[n_] := DivisorSum[n, # &, MemberQ[{1}, Mod[n/#, 4]] &] - DivisorSum[n, # &, MemberQ[{3}, Mod[n/#, 4]] &]; a[n_] := DivisorSum[n, A050469[#] &]; Table[a[n], {n, 1, 65}]

CROSSREFS

Cf. A000203, A050469, A101455, A167181 (fixed points), A262209, A288417, A327123.

Sequence in context: A225851 A107470 A228325 * A071042 A128053 A063212

Adjacent sequences:  A327119 A327120 A327121 * A327123 A327124 A327125

KEYWORD

nonn,mult

AUTHOR

Ilya Gutkovskiy, Sep 14 2019

STATUS

approved

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Last modified January 26 11:22 EST 2022. Contains 350598 sequences. (Running on oeis4.)