

A025339


Numbers that are the sum of 3 distinct nonzero squares in exactly one way.


6



14, 21, 26, 29, 30, 35, 38, 41, 42, 45, 46, 49, 50, 53, 54, 56, 59, 61, 65, 66, 70, 75, 78, 81, 83, 84, 91, 93, 104, 106, 107, 109, 113, 114, 115, 116, 118, 120, 121, 133, 137, 139, 140, 142, 145, 147, 152, 153, 157, 162, 164, 168, 169, 171, 178, 180, 184, 190, 196, 198, 200
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OFFSET

1,1


COMMENTS

Numbers n such that there is a unique triple (i,j,k) with 0 < i < j < k and n = i^2 + j^2 + k^2.
By removing the terms that have a factor of 4 we obtain A096017.  T. D. Noe, Jun 15 2004


LINKS

Robert Israel, Table of n, a(n) for n = 1..1019
Index entries for sequences related to sums of squares


EXAMPLE

14 is a term since 14 = 1^2+2^2+3^2.
38 is a term since 38 = 2^2+3^2+5^2 (note that 38 is also 1^2+1^2+6^2, but that is not a contradiction since here i=j).


MAPLE

N:= 10^4; # to get all terms <= N
S:= Vector(N):
for a from 1 to floor(sqrt(N/3)) do
for b from a+1 to floor(sqrt((Na^2)/2)) do
c:= [$(b+1) .. floor(sqrt(Na^2b^2))]:
v:= map(t > a^2 + b^2 + t^2, c):
S[v]:= map(`+`, S[v], 1)
od od:
select(t > S[t]=1, [$1..N]); # Robert Israel, Jan 03 2016


MATHEMATICA

Select[Range[200], (pr = PowersRepresentations[#, 3, 2]; Length[Select[pr, Union[#] == # && #[[1]] > 0&]] == 1)&] (* JeanFrançois Alcover, Feb 27 2019 *)


CROSSREFS

A subsequence of A004432.
Cf. A001974, A024803, A096017.
A274226 has a somewhat similar definition but is actually a different sequence.
Sequence in context: A001944 A024803 A004432 * A224771 A096017 A274226
Adjacent sequences: A025336 A025337 A025338 * A025340 A025341 A025342


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



