# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a301981 Showing 1-1 of 1 %I A301981 #12 Mar 31 2018 05:22:59 %S A301981 1,1,4,8,19,37,84,154,313,581,1109,2001,3696,6518,11637,20215,35173, %T A301981 60007,102404,171960,288286,477586,788527,1289539,2101394,3396594, %U A301981 5469267,8747285,13934572,22068218,34815513,54640049,85434022,132964684,206193983,318414629 %N A301981 Euler transform of A034448. %H A301981 Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 %F A301981 G.f.: Product_{k>=1} 1/(1-x^k)^A034448(k). %F A301981 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 A301981 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 A301981 Cf. A001615, A034448, A156303, A301594, A301982. %K A301981 nonn %O A301981 0,3 %A A301981 _Vaclav Kotesovec_, Mar 30 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE