|
%I #15 Feb 27 2018 16:27:12
%S 1,0,1,1,2,3,4,8,11,19,28,47,72,116,182,289,460,724,1153,1820,2891,
%T 4572,7249,11482,18190,28821,45651,72338,114582,181549,287596,455647,
%U 721847,1143588,1811748,2870239,4547232,7203907,11412882,18080833,28644680,45380392,71894054,113898439,180443915,285869028,452888824,717490903,1136687237
%N Expansion of 1/(1 - Sum_{k>=2} floor(1/omega(k))*x^k), where omega(k) is the number of distinct prime factors (A001221).
%C Number of compositions (ordered partitions) into prime powers (1 excluded).
%H G. C. Greubel, <a href="/A280195/b280195.txt">Table of n, a(n) for n = 0..1000</a>
%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_{k>=2} floor(1/omega(k))*x^k).
%e a(6) = 4 because we have [4, 2], [3, 3], [2, 4] and [2, 2, 2].
%t nmax = 48; CoefficientList[Series[1/(1 - Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
%Y Cf. A001221, A023360, A023894, A246655.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Dec 28 2016
|
