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%I #4 Feb 05 2017 13:17:09
%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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