A309762 - OEIS

%I #15 Jul 31 2021 18:28:57

%S 2673,6578,16562,28593,35378,42768,43218,54977,94178,105248,106353,

%T 122018,134162,137633,149058,171138,177042,178737,181202,195122,

%U 195858,198497,216513,234273,235298,235553,264113,264992,300833,318402,318882,324818,334802,346673

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

%H Robert Israel, <a href="/A309762/b309762.txt">Table of n, a(n) for n = 1..1616</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>

%e 2673 = 2^4 + 4^4 + 7^4 = 3^4 + 6^4 + 6^4, so 2673 is in the sequence.

%p N:= 10^6: # for terms <= N

%p V:= Vector(N,datatype=integer[4]):

%p for a from 1 while a^4 <= N do

%p   for b from 1 to a while a^4+b^4 <= N do

%p     for c from 1 to b do

%p       v:= a^4+b^4+c^4;

%p       if v > N then break fi;

%p       V[v]:= V[v]+1

%p od od od:

%p select(i -> V[i]>1, [$1..N]); # _Robert Israel_, Aug 19 2019

%t Select[Range@350000, Length@Select[PowersRepresentations[#, 3, 4], ! MemberQ[#, 0] &] > 1 &]

%Y Cf. A003337, A008917, A018786, A024796, A193243, A309763, A344192, A344239, A345010.

%K nonn

%O 1,1

%A _Ilya Gutkovskiy_, Aug 15 2019