A025303 Numbers that are the sum of 2 distinct nonzero squares in exactly 2 ways.

65, 85, 125, 130, 145, 170, 185, 205, 221, 250, 260, 265, 290, 305, 340, 365, 370, 377, 410, 442, 445, 481, 485, 493, 500, 505, 520, 530, 533, 545, 565, 580, 585, 610, 625, 629, 680, 685, 689, 697, 730, 740, 745, 754, 765, 785, 793, 820, 865, 884, 890, 901, 905, 949

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Numbers with exactly 2 distinct prime divisors of the form 4k+1, each with multiplicity one, or with only one prime divisor of this form with multiplicity 3, and with no prime divisor of the form 4k+3 to an odd multiplicity. - Jean-Christophe Hervé, Dec 01 2013

Examples

			65 = 5*13 = 64+1 = 49 + 16; 85 = 5*17 = 81+4 = 49+16; 125 = 5^3 = 121+4 = 100+25; 130 = 2*5*13 = 121+9 = 81+49. - _Jean-Christophe Hervé_, Dec 01 2013
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A001481, A004431, A004018, A230779 (one way).

Cf. analogs for square decompositions: A084645, A084646, A084647, A084648, A084649.

Programs

Mathematica

nn = 949; t = Table[0, {nn}]; lim = Floor[Sqrt[nn - 1]]; Do[num = i^2 + j^2; If[num <= nn, t[[num]]++], {i, lim}, {j, i - 1}]; Flatten[Position[t, 2]] (* T. D. Noe, Apr 07 2011 *)

Formula

A004018(a(n)) = 16. - Jean-Christophe Hervé, Dec 01 2013