A072389 Numbers of the form x*(x+1) * y*(y+1) ("bipronics") with x and y nonnegative integers.

0, 4, 12, 24, 36, 40, 60, 72, 84, 112, 120, 144, 180, 220, 240, 252, 264, 312, 336, 360, 364, 400, 420, 432, 480, 504, 540, 544, 600, 612, 660, 672, 684, 760, 792, 840, 864, 900, 924, 936, 1012, 1080, 1092, 1104, 1120, 1200, 1260, 1300, 1320

Offset: 1

Author

Stuart M. Ellerstein (ellerstein(AT)aol.com), Jul 20 2002

Keywords

• nonn
• easy

Comments

Nonnegative numbers k = a*b = c*d, where a+b = c+d+1. - Yifan Xie, Jun 28 2024

Examples

			a(3) = 1*2*2*3 = 12.
		

Links

• John Drake, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053990 (sequence of bipronics with x and y distinct).

Cf. A085780 (one quarter of this).

Programs

PARI

A003056(n)=(sqrtint(8*n+1)-1)\2
list(lim)=my(v=List([0]), t); for(a=1, A003056(lim\4), t=a*(a+1); for(b=a, A003056(lim\t\2), listput(v, b*(b+1)*t))); Set(v) \\ Charles R Greathouse IV, Jul 11 2024

Extensions

More terms from James Sellers, Jul 23 2002