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%I #5 Jan 18 2017 21:44:28
%S 1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,2,0,1,0,0,1,0,1,0,0,1,1,1,1,0,1,1,
%T 1,1,0,0,1,0,1,1,0,2,0,2,1,1,1,0,1,1,1,1,0,1,1,1,3,0,3,0,1,2,0,2,0,0,
%U 2,1,2,1,0,2,1,3,1,2,0,2,1,1,2,0,2,1,3,2,2,1,1,2,2,2,2,0,3,0,2,2,1,4,1,3,2,3,2,2,1,2,3
%N Expansion of Product_{j>=1} (1 + x^(Sum_{i=1..j} prime(i))).
%C Number of partitions of n into distinct nonzero partial sums of primes (A007504).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>
%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.: Product_{j>=1} (1 + x^(Sum_{i=1..j} prime(i))).
%e a(17) = 2 because we have [17] and [10, 5, 2], where 2 = prime(1), 5 = prime(1) + prime(2), 10 = prime(1) + prime(2) + prime(3), 17 = prime(1) + prime(2) + prime(3) + prime(4).
%t nmax = 110; CoefficientList[Series[Product[1 + x^Sum[Prime[i], {i, 1, j}], {j, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000586, A000607, A007504, A281273.
%K nonn
%O 0,18
%A _Ilya Gutkovskiy_, Jan 18 2017