%I #7 Apr 03 2017 20:37:31

%S 1,0,0,0,1,0,0,0,2,1,0,0,3,2,0,0,6,5,1,0,10,10,3,0,18,23,9,2,31,46,22,

%T 6,56,94,56,19,101,184,129,50,185,364,293,134,344,708,638,332,651,

%U 1378,1375,805,1265,2665,2901,1878,2503,5161,6057,4306,5061,10005,12488,9653,10384,19461,25556,21319

%N Expansion of 1/(1 - Sum_{p prime, k>=2} x^(p^k)).

%C Number of compositions (ordered partitions) of n into proper prime powers (A246547).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePower.html">Prime Power</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%F G.f.: 1/(1 - Sum_{p prime, k>=2} x^(p^k)).

%e a(12) = 3 because we have [8, 4], [4, 8] and [4, 4, 4].

%t nmax = 67; CoefficientList[Series[1/(1 - Sum[Sign[PrimeOmega[k] - 1] Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]

%o (PARI) x='x+O('x^68); Vec(1/(1 - sum(k=2, 67, sign(bigomega(k) - 1) * (1\omega(k)) * x^k))) \\ _Indranil Ghosh_, Apr 03 2017

%Y Cf. A246547, A280195, A280200, A280543, A280586.

%K nonn

%O 0,9

%A _Ilya Gutkovskiy_, Jan 06 2017