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

2673, 6578, 16562, 28593, 35378, 42768, 43218, 54977, 94178, 105248, 106353, 122018, 134162, 137633, 149058, 171138, 177042, 178737, 181202, 195122, 195858, 198497, 216513, 234273, 235298, 235553, 264113, 264992, 300833, 318402, 318882, 324818, 334802, 346673

Offset: 1

Author

Ilya Gutkovskiy, Aug 15 2019

Keywords

• nonn

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..1616
• Eric Weisstein's World of Mathematics, Biquadratic Number

Crossrefs

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

Programs

Maple

N:= 10^6: # for terms <= N
V:= Vector(N,datatype=integer[4]):
for a from 1 while a^4 <= N do
  for b from 1 to a while a^4+b^4 <= N do
    for c from 1 to b do
      v:= a^4+b^4+c^4;
      if v > N then break fi;
      V[v]:= V[v]+1
od od od:
select(i -> V[i]>1, [$1..N]); # Robert Israel, Aug 19 2019

Mathematica

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