A135060 a(n) is the smallest number m for which none of the first n multiples of m has twice as many divisors as m.

1, 2, 6, 12, 60, 120, 840, 840, 2520, 2520, 27720, 55440, 720720, 720720, 1081080, 2162160, 36756720, 36756720, 698377680, 698377680, 698377680, 698377680, 16062686640, 48188059920, 160626866400, 160626866400, 160626866400

Offset: 1

Author

J. Lowell, Feb 11 2008, Jul 08 2008, Jul 14 2008

Keywords

• nonn

Comments

a(n) is smallest integer m such that A129902(m)/m > n.

Conjecture: every number in this sequence is also in A002182. [J. Lowell disproved this conjecture at a(24) = 48188059920. - Ray Chandler]

The conjecture that every term is a multiple of the preceding term is disproved at n = 15; a(15) = 1081080, which is not a multiple of a(14) = 720720. - J. Lowell, Jun 06 2008

Examples

			60 is not a(6) because 60 has 12 divisors and 60*6=360 has 12*2=24 divisors.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..130.

Extensions

More terms from J. Lowell, May 13 2009

Inequality in the comment corrected and a(16) added by R. J. Mathar, Nov 04 2009

Extended by Ray Chandler, Nov 10 2009