A284833 - OEIS

%I #9 Apr 05 2017 04:47:05

%S 0,1,1,2,2,5,3,7,6,11,8,17,12,22,21,28,27,41,35,53,52,66,66,90,85,112,

%T 114,140,143,182,180,219,236,269,291,342,353,417,444,508,540,625,657,

%U 751,812,901,974,1097,1168,1313,1414,1562,1684,1874,2008,2219,2397,2626,2832,3121,3341,3668,3956,4305,4650

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

%C Total number of largest parts in all partitions of n into prime parts.

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

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

%e a(10) = 11 because we have [7, 3], [5, 5], [5, 3, 2], [3, 3, 2, 2], [2, 2, 2, 2, 2] and 1 + 2 + 1 + 2 + 5 = 11.

%t nmax = 65; Rest[CoefficientList[Series[Sum[x^Prime[i]/(1 - x^Prime[i]) Product[1/(1 - x^Prime[j]), {j, 1, i}], {i, 1, nmax}], {x, 0, nmax}], x]]

%o (PARI) x='x+O('x^66); concat([0], Vec(sum(i=1, 66, x^prime(i)/(1 - x^prime(i)) * prod(j=1,i, 1/(1 - x^prime(j)))))) \\ _Indranil Ghosh_, Apr 04 2017

%Y Cf. A000607, A046746, A084993, A092311, A281544, A284827.

%K nonn

%O 1,4

%A _Ilya Gutkovskiy_, Apr 03 2017