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%I #14 Aug 17 2015 00:46:37
%S 0,0,1,1,0,2,0,2,2,2,3,1,3,2,3,3,3,4,3,3,3,4,3,4,3,4,4,4,5,4,5,4,4,4,
%T 5,4,5,4,5,5,5,6,5,5,5,6,5,6,5,6,5,6,5,6,5,6,6,6,7
%N a(n) is the maximum number of distinct primes whose sum is n.
%C a(A007504(k)) = k.
%C a(n) < k when n < A007504(k).
%C Let pi(j) be the j-th prime. Then a(A007504(k) - pi(j)) = k-1, j<=k. For example, k=5: A007504(5) = 28, pi(5)=11. So a(n)=4, n = {26,25,23,21,17}.
%C Similarly, a(A007504(k) + pi(j)) = k+1, where j>k and A007504(k) + pi(j) < A007504(k+2). For example, k=8: A007504(8) = 77, A007504(10) = 129 and pi(8)=19. Therefore, a(n)=9, n = {100,106,108,114,118,120,124}.
%e a(26)=4 because 3+5+7+11 = 26. Note that some terms may be expressed in multiple ways. For example, a(47)=6: 2+3+5+7+11+19 and 2+3+5+7+13+17 = 47.
%Y Cf. A000040 (prime numbers), A007504.
%K nonn,easy
%O 0,6
%A _Bob Selcoe_, Aug 10 2015
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