The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A138570 Numbers that set records for the number by which they must be multiplied to double the number of divisors. 2
 1, 2, 6, 12, 60, 120, 840, 2520, 27720, 55440, 720720, 1081080, 2162160, 36756720, 698377680, 16062686640, 48188059920, 160626866400, 240940299600, 6987268688400, 216605329340400, 288807105787200, 1010824870255200 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 14 18:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)