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A232438 Squares or double-squares that are the sum of two distinct nonzero squares in exactly one way. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A169860 A224670 A045195 * A034025 A253017 A042236

Adjacent sequences:  A232435 A232436 A232437 * A232439 A232440 A232441

KEYWORD

nonn

AUTHOR

Jean-Christophe Hervé, Dec 01 2013

STATUS

approved

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Last modified April 19 11:00 EDT 2019. Contains 322259 sequences. (Running on oeis4.)