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A138570
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Numbers that set records for the number by which they must be multiplied to double the number of divisors.
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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
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OFFSET
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1,2
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COMMENTS
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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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EXAMPLE
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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.
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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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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(1) to a(8) verified and a(9) to a(12) added by Alonso del Arte, Oct 25 2009
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STATUS
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approved
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