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

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1616

Eric Weisstein's World of Mathematics, Biquadratic Number

Example

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

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 &]

Crossrefs

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

Sequence in context: A252301 A250855 A235253 * A344192 A345896 A085559

Adjacent sequences: A309759 A309760 A309761 * A309763 A309764 A309765

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 15 2019

Status

approved