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%I #5 Apr 03 2017 20:33:14
%S 0,1,1,2,2,5,4,6,9,11,13,18,20,26,34,37,47,55,66,80,96,111,130,150,
%T 180,206,240,278,318,366,419,483,549,626,716,803,913,1034,1167,1314,
%U 1477,1659,1861,2085,2332,2605,2902,3232,3602,3999,4442,4930,5454,6034,6675,7375,8133,8967,9870,10855
%N Expansion of Sum_{i>=1} x^prime(i)/(1 - x^prime(i)) * Product_{j>=i} 1/(1 - x^prime(j)).
%C Total number of smallest 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>=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 = 60; Rest[CoefficientList[Series[Sum[x^Prime[i]/(1 - x^Prime[i]) Product[1/(1 - x^Prime[j]), {j, i, nmax}], {i, 1, nmax}], {x, 0, nmax}], x]]
%Y Cf. A000607, A084993, A092268, A092269, A195820, A284828.
%K nonn
%O 1,4
%A _Ilya Gutkovskiy_, Apr 03 2017
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