A284834 - OEIS

%I #7 Apr 05 2017 04:47:12

%S 0,0,1,0,1,2,1,1,3,3,2,5,4,4,9,5,6,12,8,11,17,12,14,23,19,21,29,27,29,

%T 41,37,36,56,49,55,72,62,74,91,90,96,116,117,125,155,149,162,195,194,

%U 215,246,248,270,311,324,344,389,406,435,494,509,546,615,636,694,763,787,861,942,994,1063

%N Expansion of Sum_{i>=2} x^prime(i)/(1 - x^prime(i)) * Product_{j=2..i} 1/(1 - x^prime(j)).

%C Total number of largest parts in all partitions of n into odd prime parts (A065091).

%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>

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

%e a(16) = 5 because we have [13, 3], [11, 5], [7, 3, 3, 3], [5, 5, 3, 3] and 1 + 1 + 1 + 2 = 5.

%t nmax = 64; Rest[CoefficientList[Series[Sum[x^Prime[i]/(1 - x^Prime[i]) Product[1/(1 - x^Prime[j]), {j, 2, i}], {i, 2, nmax}], {x, 0, nmax}], x]]

%o (PARI) x='x+O('x^70); concat([0, 0], Vec(sum(i=2, 70, x^prime(i)/(1 - x^prime(i)) * prod(j=2,i, 1/(1 - x^prime(j)))))) \\ _Indranil Ghosh_, Apr 04 2017

%Y Cf. A046746, A065091, A084993, A092311, A099773, A284828.

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, Apr 03 2017