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

1,2

Comments

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

Links

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

Example

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.

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 ]

Crossrefs

Cf. A135060.

Sequence in context: A072486 A096123 A081125 * A161887 A139315 A014767

Adjacent sequences: A138567 A138568 A138569 * A138571 A138572 A138573

Keyword

nonn

Author

J. Lowell, May 12 2008

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

Status

approved