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

1,1

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.

Links

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

Formula

A004018(a(n)) = 12.

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

Example

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

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 *)

Crossrefs

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

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

Sequence in context: A224670 A379831 A045195 * A360017 A034025 A253017

Adjacent sequences: A232435 A232436 A232437 * A232439 A232440 A232441

Keyword

nonn

Author

Jean-Christophe Hervé, Dec 01 2013

Status

approved