%I #4 Feb 05 2017 13:17:04
%S 0,1,1,3,5,9,18,29,55,91,163,274,472,798,1349,2275,3804,6380,10614,
%T 17685,29318,48584,80296,132506,218329,359139,590092,968120,1586707,
%U 2597349,4247619,6939353,11326636,18471726,30099313,49008929,79739345,129650164,210661777,342080831,555153086,900432434,1459670289
%N Expansion of Sum_{p prime, i>=1} x^(p^i) / (1 - Sum_{p prime, j>=1} x^(p^j))^2.
%C Total number of parts in all compositions (ordered partitions) of n into prime powers (1 excluded).
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: Sum_{p prime, i>=1} x^(p^i) / (1 - Sum_{p prime, j>=1} x^(p^j))^2.
%e a(7) = 18 because we have [7], [5, 2], [4, 3], [3, 4], [3, 2, 2], [2, 5], [2, 3, 2], [2, 2, 3] and 1 + 2 + 2 + 2 + 3 + 2 + 3 + 3 = 18.
%t nmax = 43; Rest[CoefficientList[Series[Sum[Floor[1/PrimeNu[i]] x^i, {i, 2, nmax}]/(1 - Sum[Floor[1/PrimeNu[j]] x^j, {j, 2, nmax}])^2, {x, 0, nmax}], x]]
%Y Cf. A121304, A246655, A280195.
%K nonn
%O 1,4
%A _Ilya Gutkovskiy_, Jan 31 2017