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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 20 2018
STATUS
approved