The Kempner Function

The Kempner Function, applied to a composite number, permits to find the smallest integer greater than zero whose factorial is exactly divided by the number.

kempner(6) ➞ 3

1! = 1 % 6 > 0
2! = 2 % 6 > 0
3! = 6 % 6 === 0

kempner(10) ➞ 5

1! = 1 % 10 > 0
2! = 2 % 10 > 0
3! = 6 % 10 > 0
4! = 24 % 10 > 0
5! = 120 % 10 === 0

A Kempner Function applied to a prime will always return the prime itself.

kempner(2) ➞ 2
kempner(5) ➞ 5

Given an integer n, implement a Kempner Function.

Examples

kempner(6) ➞ 3

kempner(10) ➞ 5

kempner(2) ➞ 2

Notes

• Try solving this recursively, with an approach oriented to higher-order functions.
• If you need to get more confident with recursion and factorials, try this challenge.