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A309762 Numbers that are the sum of 3 nonzero 4th powers in more than one way.

%I A309762 #16 Feb 16 2025 08:33:55
%S A309762 2673,6578,16562,28593,35378,42768,43218,54977,94178,105248,106353,
%T A309762 122018,134162,137633,149058,171138,177042,178737,181202,195122,
%U A309762 195858,198497,216513,234273,235298,235553,264113,264992,300833,318402,318882,324818,334802,346673
%N A309762 Numbers that are the sum of 3 nonzero 4th powers in more than one way.
%H A309762 Robert Israel, <a href="/A309762/b309762.txt">Table of n, a(n) for n = 1..1616</a>
%H A309762 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>
%e A309762 2673 = 2^4 + 4^4 + 7^4 = 3^4 + 6^4 + 6^4, so 2673 is in the sequence.
%p A309762 N:= 10^6: # for terms <= N
%p A309762 V:= Vector(N,datatype=integer[4]):
%p A309762 for a from 1 while a^4 <= N do
%p A309762   for b from 1 to a while a^4+b^4 <= N do
%p A309762     for c from 1 to b do
%p A309762       v:= a^4+b^4+c^4;
%p A309762       if v > N then break fi;
%p A309762       V[v]:= V[v]+1
%p A309762 od od od:
%p A309762 select(i -> V[i]>1, [$1..N]); # _Robert Israel_, Aug 19 2019
%t A309762 Select[Range@350000, Length@Select[PowersRepresentations[#, 3, 4], ! MemberQ[#, 0] &] > 1 &]
%Y A309762 Cf. A003337, A008917, A018786, A024796, A193243, A309763, A344192, A344239, A345010.
%K A309762 nonn
%O A309762 1,1
%A A309762 _Ilya Gutkovskiy_, Aug 15 2019