%I #12 Mar 31 2018 05:22:59

%S 1,1,4,8,19,37,84,154,313,581,1109,2001,3696,6518,11637,20215,35173,

%T 60007,102404,171960,288286,477586,788527,1289539,2101394,3396594,

%U 5469267,8747285,13934572,22068218,34815513,54640049,85434022,132964684,206193983,318414629

%N Euler transform of A034448.

%H Vaclav Kotesovec, <a href="/A301981/b301981.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: Product_{k>=1} 1/(1-x^k)^A034448(k).

%F Conjecture: a(n) ~ exp((3*Pi*n)^(2/3)/2 - 1/2) * A^6 / (2 * 3^(5/6) * Pi^(1/3) * n^(5/6)), where A is the Glaisher-Kinkelin constant A074962.

%t nmax = 40; A034448 = Flatten[{1, Table[Times @@ (1 + Power @@@ FactorInteger[k]), {k, 2, nmax+1}]}]; CoefficientList[Series[Exp[Sum[Sum[A034448[[k]] * x^(j*k) / j, {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x]

%Y Cf. A001615, A034448, A156303, A301594, A301982.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Mar 30 2018