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A072389
Numbers of the form x*(x+1) * y*(y+1) ("bipronics") with x and y nonnegative integers.
7
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
1,2
COMMENTS
Nonnegative numbers k = a*b = c*d, where a+b = c+d+1. - Yifan Xie, Jun 28 2024
EXAMPLE
a(3) = 1*2*2*3 = 12.
PROG
(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
CROSSREFS
Cf. A053990 (sequence of bipronics with x and y distinct).
Cf. A085780 (one quarter of this).
Sequence in context: A008077 A301265 A285350 * A218391 A297568 A353795
KEYWORD
nonn,easy
AUTHOR
Stuart M. Ellerstein (ellerstein(AT)aol.com), Jul 20 2002
EXTENSIONS
More terms from James A. Sellers, Jul 23 2002
STATUS
approved