A280200 - OEIS

A280200

Expansion of 1/(1 - Sum_{k>=2} floor(1/omega(2*k-1))*x^(2*k-1)), where omega() is the number of distinct prime factors (A001221).

%I #9 Apr 25 2017 10:02:46

%S 1,0,0,1,0,1,1,1,2,2,3,4,5,7,9,11,16,21,26,37,47,61,84,108,143,191,

%T 249,331,437,575,763,1004,1326,1754,2311,3055,4036,5323,7033,9288,

%U 12257,16193,21379,28223,37278,49212,64984,85815,113297,149614,197551,260839,344439,454795,600517,792958,1047023,1382519,1825533,2410456,3182845

%N Expansion of 1/(1 - Sum_{k>=2} floor(1/omega(2*k-1))*x^(2*k-1)), where omega() is the number of distinct prime factors (A001221).

%C Number of compositions (ordered partitions) into odd prime powers (1 excluded).

%H G. C. Greubel, <a href="/A280200/b280200.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(2*k-1))*x^(2*k-1)).

%e a(10) = 3 because we have [7, 3], [5, 5] and [3, 7].

%t nmax = 60; CoefficientList[Series[1/(1 - Sum[Floor[1/PrimeNu[2 k - 1]] x^(2 k - 1), {k, 2, nmax}]), {x, 0, nmax}], x]

%Y Cf. A001221, A023359, A061345, A246655, A280151, A280195.

%K nonn

%O 0,9

%A _Ilya Gutkovskiy_, Dec 28 2016