A273545 Least number k such that k*n is the sum of two nonzero squares in exactly n ways.

2, 25, 975, 1105, 1625, 16575, 739375, 27625, 71825, 27625, 58093750, 480675, 93925, 8547175, 1077375, 801125, 76765625, 2082925, 783935546875, 801125, 942703125, 23740234375, 1404178750, 17784975, 12138425, 8300781250, 106229175, 700984375, 221252441406250

Offset: 1

Author

Altug Alkan, May 26 2016

Keywords

• nonn

Examples

			a(2) = 25 because 25*2 = 50 is the least even number that is the sum of two nonzero squares in exactly 2 ways; 50 = 1^2 + 7^2 = 5^2 + 5^2.
		

Crossrefs

Cf. A006339, A016032, A025426, A273238.

Programs

Mathematica

nR[n_] := (SquaresR[2, n] + Plus @@ Pick[{-4, 4}, IntegerQ /@ Sqrt[{n, n/2}]])/8; a[n_] := Block[{k=1}, While[nR[n * k] != n, k++]; k]; Array[a, 10] (* Giovanni Resta, May 27 2016 *)

Extensions

a(6)-a(29) from Giovanni Resta, May 26 2016