

A257409


Values of n such that there are exactly 2 solutions to x^2  y^2 = n, with x > y >= 0.


3



9, 15, 16, 21, 24, 25, 27, 32, 33, 35, 36, 39, 40, 49, 51, 55, 56, 57, 60, 65, 69, 77, 84, 85, 87, 88, 91, 93, 95, 100, 104, 108, 111, 115, 119, 121, 123, 125, 129, 132, 133, 136, 140, 141, 143, 145, 152, 155, 156, 159, 161, 169, 177, 183, 184, 185, 187, 196
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OFFSET

1,1


COMMENTS

A subsequence of A058957. Terms in the latter but not here are 45, 48, 63, 64, 72, 75, 80, 81, 96, 99, ...  M. F. Hasler, Apr 22 2015


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000


EXAMPLE

9 is in the sequence because there are 2 solutions to x^2  y^2 = 9, namely (x,y) = (3,0), (5,4).


MATHEMATICA

r[n_] := Reduce[x^2  y^2 == n && x > y >= 0, {x, y}, Integers]; Reap[For[n = 1, n < 200, n++, rn = r[n]; If[rn[[0]] === Or && Length[rn] == 2, Print[n]; Sow[n]]]][[2, 1]] (* JeanFrançois Alcover, Apr 22 2015 *)


PROG

(PARI) is_A257409(n)={A034178(n)==2} \\ M. F. Hasler, Apr 22 2015


CROSSREFS

Cf. A257408, A257410A257417.
Cf. A058957, A034178.
Sequence in context: A184048 A284128 A058957 * A105882 A136410 A324879
Adjacent sequences: A257406 A257407 A257408 * A257410 A257411 A257412


KEYWORD

nonn


AUTHOR

Colin Barker, Apr 22 2015


STATUS

approved



