Kempner function
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In number theory, the Kempner function [1] is defined for a given positive integer
to be the smallest number
such that
divides the factorial
. For example, the number
does not divide
,
, or
, but does divide
, so
.
This function has the property that it has a highly inconsistent growth rate: it grows linearly on the prime numbers but only grows sublogarithmically at the factorial numbers.