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A318368 a(n) = Sum_{d|n} (-1)^(n/d+1)*d*2^(d-1). 0
1, 3, 13, 27, 81, 183, 449, 987, 2317, 5043, 11265, 24399, 53249, 114243, 245853, 523227, 1114113, 2357175, 4980737, 10480587, 22020557, 46126083, 96468993, 201302799, 419430481, 872361987, 1811941645, 3757981275, 7784628225, 16105886823, 33285996545, 68718951387, 141733932045 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..33.

FORMULA

G.f.: Sum_{k>=1} k*2^(k-1)*x^k/(1 + x^k).

L.g.f.: log(Product_{k>=1} (1 + x^k)^(2^(k-1))) = Sum_{n>=1} a(n)*x^n/n.

a(n) ~ n * 2^(n-1). - Vaclav Kotesovec, Aug 25 2018

MATHEMATICA

Table[Sum[(-1)^(n/d + 1) d 2^(d - 1), {d, Divisors[n]}], {n, 33}]

nmax = 33; Rest[CoefficientList[Series[Sum[k 2^(k - 1) x^k/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]]

nmax = 33; Rest[CoefficientList[Series[Log[Product[(1 + x^k)^(2^(k - 1)), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]]

PROG

(PARI) a(n) = sumdiv(n, d, (-1)^(n/d+1)*d*2^(d-1)); \\ Michel Marcus, Aug 25 2018

CROSSREFS

Cf. A001787, A054599, A083413, A098407.

Sequence in context: A031011 A271625 A099062 * A196014 A266215 A192535

Adjacent sequences: A318365 A318366 A318367 * A318369 A318370 A318371

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 24 2018

STATUS

approved

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Last modified January 28 17:08 EST 2023. Contains 359895 sequences. (Running on oeis4.)