Divisibility of Harmonic Number Denominators
Problem 541
The nth harmonic number Hn is defined as the sum of the multiplicative inverses of the first n positive integers, and can be written as a reduced fraction an/bn.
, with .
, with .
Let M(p) be the largest value of n such that bn is not divisible by p.
For example, M(3) = 68 because , b68=2933773379069966367528193600 is not divisible by 3, but all larger harmonic numbers have denominators divisible by 3.
You are given M(7) = 719102.
Find M(137).