A139719 A number m is included if k + m/k divides m for at least one divisor k of m.

4, 16, 18, 36, 48, 64, 72, 100, 144, 150, 162, 180, 192, 196, 256, 288, 294, 324, 400, 432, 448, 450, 484, 490, 576, 588, 600, 648, 676, 720, 768, 784, 882, 900, 960, 1024, 1134, 1152, 1156, 1176, 1200, 1210, 1296, 1350, 1444, 1458, 1584, 1600, 1620, 1728

Offset

1,1

Comments

All terms are even. All even perfect squares are included. If m is included, then 4m is also included.

Also the set of all numbers m of the form m = r*s*(r+s)^2*t^2 with positive integers r,s,t; if one additionally requires (r,s) = 1 and r <= s, then there is exactly one such representation for each m. [From Hagen von Eitzen, Jul 22 2009]

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

72 is included because 6 is a divisor of 72 and (6 + 72/6) = 18 divides 72.

Mathematica

nkdQ[n_]:=Module[{divs=Most[Divisors[n]]}, MemberQ[Divisible[n, #]&/@ (#+n/#&/@ divs), True]]; Select[Range[2000], nkdQ] (* Harvey P. Dale, Apr 24 2012 *)

Crossrefs

Cf. A139718.

Sequence in context: A363084 A224705 A243298 * A117102 A077476 A282552

Adjacent sequences: A139716 A139717 A139718 * A139720 A139721 A139722

Keyword

nonn

Author

Leroy Quet, May 01 2008

Extensions

Extended by Ray Chandler, Jul 01 2009

Status

approved