

A309763


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


9



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
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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



