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Search: id:A138570
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| A138570 |
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Numbers that set records for the number that multiplying by will double the number of divisors. |
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+0
2
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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A number is in this sequence exactly once if and only if it is in A135060 at least once.
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LINKS
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Ray Chandler, Table of n, a(n) for n=1..52
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EXAMPLE
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840 qualifies for this sequence because 840 sets a new record (9) for the number that multiplying will double the divisors (840 has 32 divisors; smallest number with 64 divisors is 840 * 9 = 7560). 120's record of 7 is not exceeded by any number from 121 to 839.
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MATHEMATICA
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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 ]
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CROSSREFS
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Cf. A135060.
Sequence in context: A072486 A096123 A081125 this_sequence A161887 A139315 A014767
Adjacent sequences: A138567 A138568 A138569 this_sequence A138571 A138572 A138573
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KEYWORD
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nonn,new
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AUTHOR
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J. Lowell (jhbubby(AT)mindspring.com), May 12 2008
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EXTENSIONS
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a(1) to a(8) verified and a(9) to a(12) added by Alonso Delarte (alonso.delarte(AT)gmail.com), Oct 25 2009
Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 10 2009
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