A232438 Squares or double-squares that are the sum of two distinct nonzero squares in exactly one way.

25, 50, 100, 169, 200, 225, 289, 338, 400, 450, 578, 676, 800, 841, 900, 1156, 1225, 1352, 1369, 1521, 1600, 1681, 1682, 1800, 2025, 2312, 2450, 2601, 2704, 2738, 2809, 3025, 3042, 3200, 3362, 3364, 3600, 3721, 4050, 4624, 4900, 5202, 5329, 5408, 5476

Offset: 1

Author

Jean-Christophe Hervé, Dec 01 2013

Keywords

• nonn

Comments

Subsequence of A004431 and A001481.

Numbers with exactly one prime factor of form 4k+1 with multiplicity 2, and without prime factor of form 4k+3 to an odd multiplicity.

Examples

			25 = 5^2 = 16+9; 50 = 2*5^2 = 49+1.
		

Links

• Jean-Christophe Hervé and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 368 terms from Jean-Christophe Hervé)

Crossrefs

Cf. A001481, A004431, A004018, A125853 (A004018 = 4), A230779 (A004018 = 8), A025303 (A004018 = 16).

Analogs for square decompositions: A084645, A084646, A084647, A084648, A084649.

Programs

Mathematica

Select[Range[10^4], (IntegerQ[Sqrt[#]] || IntegerQ[Sqrt[#/2]]) && Count[ PowersRepresentations[#, 2, 2], {x_, y_} /; Unequal[0, x, y]] == 1 &]
(* or *) Select[Range[10^4], SquaresR[2, #] == 12 &] (* Jean-François Alcover, Dec 03 2013 *)

Formula

A004018(a(n)) = 12.

Terms are obtained by the products A125853(k)*A002144(p)^2 for k, p > 0, ordered by increasing values.