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A281853 Expansion of Sum_{k>=2} x^prime(k) / (1 - Sum_{k>=2} x^prime(k))^2. 0

%I

%S 0,0,1,0,1,2,1,4,3,6,10,8,19,22,26,48,53,78,112,136,205,264,354,504,

%T 639,890,1204,1568,2173,2868,3826,5192,6839,9214,12295,16296,21894,

%U 28996,38624,51552,68230,90930,120715,159988,212728,281696,373574,495312,655365,868510,1149161,1520020,2011591,2658416,3514446

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

%C Total number of parts in all compositions (ordered partitions) of n into odd primes (A065091).

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

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

%e a(11) = 10 because we have [11], [5, 3, 3], [3, 5, 3], [3, 3, 5] and 1 + 3 + 3 + 3 = 10.

%t nmax = 55; Rest[CoefficientList[Series[Sum[x^Prime[k], {k, 2, nmax}]/(1 - Sum[x^Prime[k], {k, 2, nmax}])^2, {x, 0, nmax}], x]]

%Y Cf. A002124, A065091, A121304.

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, Jan 31 2017

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Last modified June 14 09:06 EDT 2021. Contains 345018 sequences. (Running on oeis4.)