OFFSET
0,3
COMMENTS
Euler transform of A034444.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
N. J. A. Sloane, Transforms
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^k)^A034444(k).
G.f.: exp(Sum_{k>=1} A048250(k)*x^k/(k*(1 - x^k))).
G.f.: exp(Sum_{k>=1} Sum_{j>=1} mu(j)^2*x^(j*k)/(k*(1 - x^(j*k)))), where mu = Möbius function (A008683).
log(a(n)) ~ sqrt(2*n*log(n)). - Vaclav Kotesovec, Sep 13 2018
MAPLE
with(numtheory): a:=series(mul(1/(1-x^k)^(2^nops(factorset(k))), k=1..50), x=0, 41): seq(coeff(a, x, n), n=0..40); # Paolo P. Lava, Apr 02 2019
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[1/(1 - x^k)^(2^PrimeNu[k]), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 40; CoefficientList[Series[Exp[Sum[DivisorSum[k, # &, SquareFreeQ[#] &] x^k/(k (1 - x^k)), {k, 1, nmax}]], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d 2^PrimeNu[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 40}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 11 2018
STATUS
approved