A257415 Values of n such that there are exactly 8 solutions to x^2 - y^2 = n with x > y >= 0.

480, 576, 672, 840, 864, 945, 1056, 1080, 1120, 1155, 1248, 1296, 1320, 1365, 1485, 1512, 1536, 1560, 1600, 1632, 1755, 1760, 1785, 1824, 1848, 1995, 2025, 2040, 2079, 2080, 2145, 2184, 2208, 2280, 2295, 2376, 2415, 2457, 2464, 2560, 2565, 2625, 2720, 2760

Offset: 1

Author

Colin Barker, Apr 22 2015

Keywords

• nonn

Examples

			480 is in the sequence because there are 8 solutions to x^2 - y^2 = 480, namely (x,y) = (22,2), (23,7), (26,14), (29,19), (34,26), (43,37), (62,58), (121,119).
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1600 terms from Colin Barker)

Crossrefs

Cf. A257408, A257409, A257410, A257411, A257412, A257413, A257414, A257416, A257417.

Cf. A034178.

Programs

Mathematica

nn = 3000;
t = Table[0, {nn}];
Do[n = x^2 - y^2; If[n <= nn, t[[n]]++], {x, nn}, {y, 0, x - 1}];
Position[t, 8] // Flatten (* Jean-François Alcover, Jun 18 2020, after T. D. Noe in A034178 *)

PARI

is_A257415(n)={A034178(n)==8} \\ M. F. Hasler, Apr 22 2015