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A292459
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a(n) is the smallest number whose factorial has at least n! divisors.
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0
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0, 0, 2, 4, 6, 9, 12, 16, 20, 26, 31, 38, 43, 52, 59, 67, 74, 83, 93, 103, 111, 123, 134, 146, 157, 167, 179, 193, 203, 218, 229, 241, 258, 271, 283, 301, 313, 331, 347, 359, 379, 393, 409, 422, 440, 457, 469, 488, 504, 523, 543, 563, 577, 597, 614, 631, 651
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OFFSET
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0,3
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COMMENTS
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The ratio log(a(n))/log(n) reaches a maximum at n=51, where its value is log(563)/log(51) = 1.61077326914...; as n increases, does the ratio approach a limit of 1?
n a(n) log(a(n))/log(n)
====== ======== ================
10 31 1.49136169383...
100 1609 1.60327802204...
1000 41036 1.53772167371...
10000 761879 1.47047150077...
100000 12091591 1.41649668973...
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LINKS
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EXAMPLE
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a(5) = 9 because 9! has 160 (> 120 = 5!) divisors, while 8! has only 96 (< 120).
a(10) = 31 because 31! has 4665600 (> 3628800 = 10!) divisors, while 30! has only 2332800 (< 3628800).
a(100000) = 12091591 because 12091591! has 5.58...*10^456573 (> 2.82...*10^456573 = 100000!) divisors, while 12091590! has only 2.79...*10^456573.
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CROSSREFS
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Cf. A027423 (Number of positive divisors of n!).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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