A138570 Numbers that set records for the number by which they must be multiplied to double the number of divisors.

1, 2, 6, 12, 60, 120, 840, 2520, 27720, 55440, 720720, 1081080, 2162160, 36756720, 698377680, 16062686640, 48188059920, 160626866400, 240940299600, 6987268688400, 216605329340400, 288807105787200, 1010824870255200

Offset: 1

Author

J. Lowell, May 12 2008

Keywords

• nonn

Comments

A number is in this sequence exactly once if and only if it is in A135060 at least once.

Examples

			840 is a term of this sequence because 840 sets a new record (9) for the number by which it must be multiplied to double its number of divisors (840 has 32 divisors; the smallest number with 64 divisors is 840 * 9 = 7560).
120's record of 7 is not exceeded by any number from 121 to 839.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..52

Crossrefs

Cf. A135060.

Programs

Mathematica

f[ n_ ] := f[ n ] = Module[ {i = 2}, While[ 2 * Length[ Divisors[ n ] ] != Length[ Divisors[ i * n ] ], i++ ]; Return[ i ] ]; A138570 = {}; searchMax = 100000; currHigh = 0; i = 1; While[ i < searchMax, n = f[ i ]; If[ n > currHigh, A138570 = {A138570, i}; currHigh = n ]; i++ ]; A138570 = Flatten[ A138570 ]

Extensions

a(1) to a(8) verified and a(9) to a(12) added by Alonso del Arte, Oct 25 2009

Extended by Ray Chandler, Nov 10 2009