OFFSET
1,1
COMMENTS
Equivalently positive integers whose square is expressible in exactly one way as -x^2 + 2xy + y^2 with 0 < x < y by replacing (x,y) with (2x,x+y). As such this sequence represents the sum of legs that are unique to a single Pythagorean triangle. - Ray Chandler, Feb 18 2020
n is in the sequence iff A331671(n)=1. - Ray Chandler, Feb 26 2020
LINKS
Ray Chandler, Table of n, a(n) for n = 1..10000 (first 750 terms from Colin Barker)
EXAMPLE
7 is in the sequence because the only solution to x^2 + 6xy + y^2 = 49 with 0 < x < y is (x,y) = (2,3).
MATHEMATICA
s[n_] := Solve[0 < x < y && n^2 == x^2 + 6 x y + y^2, {x, y}, Integers];
Reap[For[n = 1, n < 200, n++, If[Length[s[n]]==1, Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Feb 13 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Colin Barker, Jan 24 2015
STATUS
approved