%I #19 Aug 03 2020 11:49:24
%S 12,43,74,105,136,167,198,229,254,260,285,291,316,322,347,353,378,384,
%T 409,440,471,496,502,527,533,558,564,589,595,620,651,682,713,738,744,
%U 769,775,800,806,831,862,893,924,955,980,986,1011,1017,1035,1042,1066,1073,1097
%N Numbers that are the sum of 12 positive 5th powers.
%H David A. Corneth, <a href="/A003357/b003357.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%e From _David A. Corneth_, Aug 03 2020: (Start)
%e 14585 is in the sequence as 14585 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 4^5 + 4^5 + 5^5 + 5^5 + 5^5 + 5^5.
%e 22088 is in the sequence as 22088 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 4^5 + 5^5 + 7^5.
%e 24800 is in the sequence as 24800 = 2^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 6^5 + 6^5. (End)
%o (PARI) (A003357_upto(N, k=12, m=5)=[n|n<-[1..#N=sum(n=1, sqrtnint(N, m), 'x^n^m, O('x^N))^k], polcoef(N, n)])(1100) \\ 2nd & 3rd optional arg allow to get other sequences of this group. See A003333 for alternate code. - _M. F. Hasler_, Aug 03 2020
%Y Cf. A000584 (fifth powers).
%Y Cf. A003347 - A003356 (numbers that are the sum of 2, ..., 11 positive 5th powers); A003335, A003346, A003368, A003379, A003390, A004801, A004812, A004823 (numbers that are the sum of 12 positive 3rd, ..., 11th powers).
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_