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A096739 Numbers k such that k^4 can be written as a sum of four distinct positive 4th powers.

%I A096739 #21 Feb 16 2025 08:32:53
%S A096739 353,651,706,1059,1302,1412,1765,1953,2118,2471,2487,2501,2604,2824,
%T A096739 2829,3177,3255,3530,3723,3883,3906,3973,4236,4267,4333,4449,4557,
%U A096739 4589,4942,4949,4974,5002,5208,5281,5295,5463,5491,5543,5648,5658,5729,5859
%N A096739 Numbers k such that k^4 can be written as a sum of four distinct positive 4th powers.
%C A096739 From _David Wasserman_, Nov 16 2007: (Start)
%C A096739 Every multiple of a term is a term.
%C A096739 Is this sequence the same as A003294? (End)
%D A096739 D. Wells, Curious and interesting numbers, Penguin Books, p. 139.
%H A096739 K. Rose and S. Brudno, <a href="http://dx.doi.org/10.1090/S0025-5718-1973-0329184-2">More about four biquadrates equal one biquadrate</a>, Math. Comp., 27 (1973), 491-494.
%H A096739 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DiophantineEquation4thPowers.html">Diophantine Equation 4th Powers</a>.
%e A096739 Example solutions:
%e A096739    353^4 =   30^4 +  120^4 +  272^4 +  315^4;
%e A096739    706^4 =   60^4 +  240^4 +  544^4 +  630^4;
%e A096739   1059^4 =   90^4 +  360^4 +  816^4 +  945^4;
%e A096739   1302^4 =  480^4 +  680^4 +  860^4 + 1198^4;
%e A096739   1412^4 =  120^4 +  480^4 + 1088^4 + 1260^4;
%e A096739   3723^4 = 2270^4 + 2345^4 + 2460^4 + 3152^4.
%Y A096739 Cf. A003294, A176197.
%K A096739 nonn
%O A096739 1,1
%A A096739 _Lekraj Beedassy_, May 30 2002
%E A096739 Corrected by Bo Asklund (boa(AT)mensa.se), Nov 05 2004
%E A096739 Corrected and extended by _David Wasserman_, Nov 16 2007