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A139315
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Smallest integer such that n*a(n) is the smallest multiple of a(n) with twice as many divisors as n, or 0 if no such number is possible.
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2
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1, 2, 6, 12, 60, 120, 1260, 840, 0, 2520, 27720, 55440, 0, 720720, 1081080, 2162160, 61261200, 36756720, 1396755360, 2327925600, 0, 698377680, 16062686640, 48188059920, 0, 749592043200, 160626866400, 240940299600, 0, 6987268688400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| Proof that a(10)=0. In order for 10*n to have twice as many divisors as n, it must be either a multiple of 20 but not of 40 or 100 (in which case 8*n has twice as many divisors) or a multiple of 50 but not of 100 or 250 (in which case 4*n has twice as many divisors.) In both cases, 10*n is not the smallest number with twice as many divisors as n and so a(10) of this sequence is 0.
Generalizing above result, a(pq)=0 for distinct primes p,q with p<q if p^2<q. - Chandler
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LINKS
| Ray Chandler, Table of n, a(n) for n=2..100
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EXAMPLE
| a(8) = 1260 because it must be a multiple of 4 but not of 8. It cannot be 4 because 4*3=12 has twice as many divisors as 4. It cannot be 12 because 12*5=60 has twice as many divisors as 12. It cannot be 60 because 60*6=360 has twice as many divisors as 60. It cannot be 180 because 180*7=1260 has twice as many divisors as 180. It must be 1260.
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CROSSREFS
| Cf. A135060.
Sequence in context: A081125 A138570 A161887 * A014767 A002319 A195307
Adjacent sequences: A139312 A139313 A139314 * A139316 A139317 A139318
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KEYWORD
| nonn
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AUTHOR
| J. Lowell (jhbubby(AT)mindspring.com), Jun 07 2008
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EXTENSIONS
| a(14)-a(100) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 03 2009
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