A174133 Integers of the form (a^2-1)*(b^2+1) where a >= 1 and b >= 0.

0, 3, 6, 8, 15, 16, 24, 30, 35, 40, 48, 51, 63, 70, 75, 78, 80, 96, 99, 111, 120, 126, 136, 143, 150, 160, 168, 175, 195, 198, 208, 224, 240, 246, 255, 286, 288, 296, 303, 315, 323, 336, 350, 360, 366, 390, 399, 400, 408, 435, 440, 448, 480, 483, 495, 510, 520

Offset: 1

Author

Max Alekseyev, Apr 01 2010

Keywords

• nonn

Comments

Numbers of the form A002522(i)*A005563(j) where i,j >= 0. - Altug Alkan, May 02 2016

Examples

			3 is a term because 3 = (2^2-1)*(0^2+1).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002522, A005563.

Programs

Maple

N:= 10000: # to get all terms <= N
S:= {0, seq(seq((a^2-1)*(b^2+1), b=0 .. floor(sqrt(N/(a^2-1)-1))),a=2..floor(sqrt(N+1)))}:
sort(convert(S,list)); # Robert Israel, May 05 2016

Mathematica

TakeWhile[#, Function[k, k < Sqrt@ Max@ #]] &@ Select[DeleteDuplicates@ Sort[(#1^2 - 1) (#2^2 + 1) & @@@ Tuples[Range[0, 25], 2]], # >= 0 &] (* Michael De Vlieger, May 02 2016 *)

Extensions

Name clarified by Altug Alkan, May 02 2016