OFFSET
0,3
COMMENTS
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...
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Sep 16 2017
STATUS
approved