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A063923 Numbers k such that k^5 = a^5 + b^5 + c^5 + d^5 + e^5 has a nontrivial primitive solution in nonnegative integers.

%I A063923 #47 Aug 20 2023 10:49:26
%S A063923 72,94,107,144,365,415,427,435,480,503,530,553,575,650,700,703,716,
%T A063923 729,744,764,804,848,851,875,923,941,975,1004,1006,1040,1044,1235,
%U A063923 1257,1313,1327,1329,1369,1392,1457,1469,1504,1528,1537,1575,1583,1588,1596,1623,1653,1685,1686
%N A063923 Numbers k such that k^5 = a^5 + b^5 + c^5 + d^5 + e^5 has a nontrivial primitive solution in nonnegative integers.
%C A063923 Primitive means a solution for k has gcd(a,b,c,d,e) = 1. [Corrected by _Jianing Song_, Jan 24 2020]
%C A063923 Nontrivial means at least two of a,b,c,d,e are nonzero. - _Jianing Song_, Jan 24 2020
%H A063923 Jianing Song, <a href="/A063923/b063923.txt">Table of n, a(n) for n = 1..400</a> (All terms from James Waldby link)
%H A063923 L. J. Lander, T. R. Parkin and J. L. Selfridge, <a href="https://www.jstor.org/stable/2003249">A Survey of Equal Sums of Like Powers</a>, Mathematics of Computation, Vol. 21, No. 99 (Jul., 1967), pp. 446-459. See Table III p. 449.
%H A063923 James Waldby, <a href="https://pat7.com/jp/s515-10007-t">A Table of Fifth Powers equal to a Fifth Power</a>
%H A063923 <a href="/index/Di#Diophantine">Index to sequences related to Diophantine equations</a> (5,1,5)
%e A063923    72^5 = 19^5 + 43^5 + 46^5 + 47^5 +  67^5;
%e A063923    94^5 = 21^5 + 23^5 + 37^5 + 79^5 +  84^5;
%e A063923   107^5 =  7^5 + 43^5 + 57^5 + 80^5 + 100^5.
%Y A063923 Cf. A063922.
%Y A063923 For cubes: A003072, A023041, A261029.
%Y A063923 For fourth powers: A003828, A175610, A039664, A003294.
%K A063923 nonn
%O A063923 1,1
%A A063923 _David W. Wilson_, Aug 31 2001
%E A063923 144 and 1006 inserted and name simplified by _Jianing Song_, Jan 24 2020
%E A063923 More terms from _Jinyuan Wang_, Jan 24 2020