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A321875 a(n) = Sum_{d|n} d*d!. 1
1, 5, 19, 101, 601, 4343, 35281, 322661, 3265939, 36288605, 439084801, 5748023639, 80951270401, 1220496112085, 19615115520619, 334764638530661, 6046686277632001, 115242726706374263, 2311256907767808001, 48658040163569088701, 1072909785605898275299 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Inverse Möbius transform of A001563.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..448

N. J. A. Sloane, Transforms

FORMULA

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

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

a(n) = Sum_{d|n} A001563(d).

MATHEMATICA

Table[Sum[d d!, {d, Divisors[n]}], {n, 21}]

nmax = 21; Rest[CoefficientList[Series[Sum[k k! x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]]

nmax = 21; Rest[CoefficientList[Series[-Log[Product[(1 - x^k)^k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]]

PROG

(PARI) a(n) = sumdiv(n, d, d*d!); \\ Michel Marcus, Nov 20 2018

(MAGMA) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&+[k*Factorial(k)*x^k/(1 - x^k): k in [1..(m+2)]]) )); // G. C. Greubel, Nov 20 2018

(Sage)

s = sum(k*factorial(k)*x^k/(1-x^k) for k in (1..24));

(s/x).series(x, 21).coefficients(x, sparse=false) # Peter Luschny, Nov 21 2018

CROSSREFS

Cf. A000142, A001563, A062363, A107895.

Sequence in context: A331336 A146144 A162292 * A005165 A071828 A280067

Adjacent sequences:  A321872 A321873 A321874 * A321876 A321877 A321878

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 20 2018

STATUS

approved

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Last modified April 6 15:41 EDT 2020. Contains 333276 sequences. (Running on oeis4.)