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%I #2 Mar 30 2012 18:40:52
%S 1,4,9,20,32,59,88,159,231,444,659,1262,1897,3814,1187707
%N Partial sums of A014597.
%C Partial sums of numbers n such that n^2 is a sum of distinct factorials. The subsequence of primes in this partial sum begins: 59, 659, 1187707. If there is a larger value (the sequence might be finite), a(n)^2 must be greater than 48! (about 1.24139 * 10^61).
%F a(n) = SUM[i=1..n] A014597(i) = SUM[i=1..n] {i such that i^2 is a sum of distinct factorials} = SUM[i=1..n] {i such that i^2 is a sum of distinct A000142(j)}.
%e a(15) = 1 + 3 + 5 + 11 + 12 + 27 + 29 + 71 + 72 + 213 + 215 + 603 + 635 + 1917 + 1183893 is prime.
%Y Cf. A000142, A014597, A025494, A051761, A059589.
%K hard,nonn
%O 1,2
%A _Jonathan Vos Post_, May 08 2010
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