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%I #7 Mar 30 2012 18:40:43
%S 0,0,0,1,1,2,1,2,2,3,3,3,2,4,3,5,3,5,6,5,6,6,5,8,6,9,6,7,10,8,9,9,8,
%T 10,8,11,8,8,13,11,10,11,11,14,10,14,13,9,17,13,12,15,13,17,11,15,17,
%U 10,17,17,14,17,16,19,12,17,19,13,18,17,14,17,17,23,16
%N Number of order-independent ways to represent 24*n+5 as the sum of squares of exactly 5 primes.
%C Hua proved in 1938 that every sufficiently large integer n congruent to 5 mod 24 can be written as the sum of the squares of exactly 5 primes.
%D L. K. Hua, Some results in the additive prime number theory, Quart J. Math., Oxford, 9 (1938) 68-80.
%H T. L. Todorova, D. I. Tolev, <a href="http://arXiv.org/abs/0711.0171">On the distribution of alpha p modulo one for primes p of a special form</a>, Nov 1, 2007.
%e a(3) = 1 because the only way, up to permutation, to represent 24*n+5 as the sum of squares of exactly 5 primes is 77 = 5 + 24*3 = 5^2 + 5^2 + 3^2 + 3^2 + 3^2.
%e a(5) = 2 because 125 = 5 + 24*5 = 5^2 + 5^2 + 5^2 + 5^2 + 5^2 = 7^2 + 7^2 + 3^2 + 3^2 + 3^2.
%e a(9) = 3 because 221 = 5 + 24*9 = 11^2 + 5^2 + 5^2 + 5^2 + 5^2 = 13^2 + 5^2 + 3^2 + 3^2 + 3^2 = 7^2 + 7^2 + 7^2 + 7^2 + 5^2.
%e a(13) = 4 because 317 = 5 + 24*13 = 11^2 + 11^2 + 5^2 + 5^2 + 5^2 = 11^2 + 7^2 + 7^2 + 7^2 + 7^2 = 13^2 + 11^2 + 3^2 + 3^2 + 3^2 = 13^2 + 7^2 + 7^2 + 5^2 + 5^2.
%e a(15) = 5 because 365 = 5 + 24*15 = 11^2 + 11^2 + 7^2 + 7^2 + 5^2 = 13^2 + 11^2 + 5^2 + 5^2 + 5^2 = 13^2 + 13^2 + 3^2 + 3^2 + 3^2 = 13^2 + 7^2 + 7^2 + 7^2 + 7^2 = 17^2 + 7^2 + 3^2 + 3^2 + 3^2.
%e a(18) = 6 because 437 = 5 + 24*18 = 11^2 + 11^2 + 11^2 + 7^2 + 5^2 = 13^2 + 11^2 + 7^2 +7^2 + 7^2 = 13^2 + 13^2 + 7^2 + 5^2 + 5^2 = 17^2 + 11^2 + 3^2 + 3^2 + 3^2 = 17^2 + 7^2 + 7^2 + 5^2 + 5^2 = 19^2 + 7^2 + 3^2 + 3^2 + 3^2 = 19^2 + 7^2 + 3^2 + 3^2 + 3^2.
%e a(23) = 8 because 557 = 5 + 24*23 = 13^2 + 11^2 + 11^2 + 11^2 + 5^2 = 13^2 + 13^2 + 11^2 + 7^2 + 7^2 = 13^2 + 13^2 + 13^2 + 5^2 + 5^2 = 17^2 + 11^2 + 7^2 + 7^2 + 7^2 = 17^2 + 13^2 + 7^2 + 5^2 + 5^2 = 19^2 + 11^2 + 5^2 + 5^2 + 5^2 = 19^2 + 13^2 + 3^2 + 3^2 + 3^2 = 19^2 + 7^2 + 7^2 + 7^2 + 7^2.
%K nonn
%O 0,6
%A _Jonathan Vos Post_ and John Sokol (john.sokol(AT)gmail.com), Nov 06 2007
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