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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 (list; graph; refs; listen; history; text; internal format)
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((N-a^2)/2)) do

    c:= [$(b+1) .. floor(sqrt(N-a^2-b^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

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

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)