A259263 Numbers of the form (m*k)^2/(m^2-k^2) for distinct integers m and k.

12, 18, 48, 72, 108, 147, 150, 162, 180, 192, 225, 240, 288, 300, 400, 405, 432, 448, 450, 578, 588, 600, 648, 720, 768, 882, 900, 960, 972, 980, 1008, 1100, 1152, 1200, 1260, 1323, 1350, 1452, 1458, 1600, 1620, 1728, 1792, 1800, 2025, 2028, 2100, 2160, 2178, 2312, 2352, 2400, 2592, 2700, 2880, 3042, 3072, 3150

Offset

1,1

Comments

The odd numbers are much more rare than even numbers: 147, 225, 405, 1323, 2025, 3645, 3675, ... For 1 <= m <= 10^4 and 1 <= k <= m, there are 9217 total solutions. Of these solutions, only 679 are odd. See A259288.

Similarly, the reciprocals of these numbers can be represented as the difference in the reciprocals of two squares (i.e., there exists two distinct integers m and k satisfying 1/a(n) = 1/m^2 - 1/k^2).

If a(n) is a square, its square root is in A111200.

Links

Table of n, a(n) for n=1..58.

Example

(3*6)^2/(6^2-3^2) = 18^2/(3*9) = 12. So 12 is a member of this sequence.

Prog

(PARI) v=[]; for(m=1, 7500, for(n=1, m-1, if(type(s=(m*n)^2/(m^2-n^2))=="t_INT", v=concat(v, s)))); vecsort(v, , 8)

Crossrefs

Cf. A063664, A111200, A259288.

Sequence in context: A133403 A152615 A258088 * A341039 A279369 A119147

Adjacent sequences: A259260 A259261 A259262 * A259264 A259265 A259266

Keyword

nonn

Author

Derek Orr, Jun 22 2015

Status

approved