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%I #4 Dec 31 2016 01:30:23
%S 1,1,2,3,3,5,5,7,8,9,11,12,14,16,18,20,23,25,29,32,36,40,44,49,54,59,
%T 65,70,76,83,89,98,105,114,123,132,143,154,165,178,190,204,219,234,
%U 251,267,285,304,324,345,368,390,415,441,468,498,527,559,591,626,663,702,742,784,828,873,923,973,1026,1081,1138
%N Expansion of (1/(1 - x))*Product_{k>=1} (1 + x^prime(k)).
%C Partial sums of A000586.
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, end of section 16.4.2 "Partitions into distinct parts", pp.348ff
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePartition.html">Prime Partition</a>
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: (1/(1 - x))*Product_{k>=1} (1 + x^prime(k)).
%t nmax = 70; CoefficientList[Series[(1/(1 - x)) Product[(1 + x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000070, A000586, A034891, A036469.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 30 2016