|
%I #8 Feb 11 2021 11:21:40
%S 1,0,1,1,3,3,8,10,23,32,64,98,187,296,543,891,1595,2660,4694,7924,
%T 13854,23556,40940,69939,121122,207490,358517,615292,1061635,1824013,
%U 3144404,5406257,9314645,16021922,27595176,47478950,81757104,140691461,242232918,416890645,717712748,1235289624
%N Expansion of 1/(1 - Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k))).
%C Invert transform of A001222.
%H Alois P. Heinz, <a href="/A300672/b300672.txt">Table of n, a(n) for n = 0..2000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F G.f.: 1/(1 - Sum_{k>=2} A001222(k)*x^k).
%p a:= proc(n) option remember; `if`(n=0, 1,
%p add(a(n-i)*numtheory[bigomega](i), i=1..n))
%p end:
%p seq(a(n), n=0..42); # _Alois P. Heinz_, Feb 11 2021
%t nmax = 41; CoefficientList[Series[1/(1 - Sum[Boole[PrimePowerQ[k]] x^k/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
%t nmax = 41; CoefficientList[Series[1/(1 - Sum[PrimeOmega[k] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
%t a[0] = 1; a[n_] := a[n] = Sum[PrimeOmega[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 41}]
%Y Cf. A001222, A022559, A112967, A129921, A180305, A293549, A300671.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Mar 11 2018
|
