A309763 Numbers that are the sum of 4 nonzero 4th powers in more than one way.

259, 2674, 2689, 2754, 2929, 3298, 3969, 4144, 4209, 5074, 6579, 6594, 6659, 6769, 6834, 7203, 7874, 8194, 8979, 9154, 9234, 10113, 10674, 11298, 12673, 12913, 13139, 14674, 14689, 14754, 16563, 16578, 16643, 16818, 17187, 17234, 17299, 17314, 17858, 18963, 19699

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Biquadratic Number

Example

259 = 1^4 + 1^4 + 1^4 + 4^4 = 2^4 + 3^4 + 3^4 + 3^4, so 259 is in the sequence.

Maple

N:= 10^5: # 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 while a^4 + b^4+ c^4 <= N do
      for d from 1 to c do
         v:= a^4+b^4+c^4+d^4;
         if v > N then break fi;
         V[v]:= V[v]+1
od od od od:
select(i -> V[i]>1, [$1..N]); # Robert Israel, Oct 07 2019

Mathematica

Select[Range@20000, Length@Select[PowersRepresentations[#, 4, 4], ! MemberQ[#, 0] &] > 1 &]

Crossrefs

Cf. A000583, A003338, A018786, A025367, A025406, A309762, A344193, A344238, A344241, A344644.

Sequence in context: A082788 A043376 A038480 * A344193 A254642 A322882

Adjacent sequences: A309760 A309761 A309762 * A309764 A309765 A309766

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 15 2019

Status

approved