A134422 Square numbers which are sums of 2 distinct nonzero squares.

25, 100, 169, 225, 289, 400, 625, 676, 841, 900, 1156, 1225, 1369, 1521, 1600, 1681, 2025, 2500, 2601, 2704, 2809, 3025, 3364, 3600, 3721, 4225, 4624, 4900, 5329, 5476, 5625, 6084, 6400, 6724, 7225, 7569, 7921, 8100, 8281, 9025, 9409, 10000, 10201

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Index entries for sequences related to sums of squares

Formula

a(n) = A009003(n)^2.

Example

25 = 5^2 = 4^2 + 3^2, and so 25 is in the sequence.
100 = 10^2 = 8^2 + 6^2, and so 100 is in the sequence.
169 = 13^2 = 12^2 + 5^2, and so 169 is in the sequence.

Mathematica

c = {}; Do[Do[k = a^2 + b^2; If[IntegerQ[Sqrt[k]], AppendTo[c, k]], {a, 1, b - 1}], {b, 200}]; Union[c] (* Artur Jasinski *)
Select[Range[100]^2, Length[PowersRepresentations[#, 2, 2]] > 1 &] (* Alonso del Arte, Feb 11 2014 *)

Prog

(PARI) select(n->for(k=1, sqrtint(n\2), if(issquare(n-k^2), return(n>k^2))); 0, vector(100, i, i^2)) \\ Charles R Greathouse IV, Jul 02 2013

Crossrefs

Cf. A000404, A000415, A009003.

Sequence in context: A353152 A335717 A198385 * A016850 A309779 A356533

Adjacent sequences: A134419 A134420 A134421 * A134423 A134424 A134425

Keyword

nonn

Author

Artur Jasinski, Oct 25 2007

Status

approved