Number divisible by a range of numbers

Given two positive integers $a$ and $b$ with $a\le b$, let $P(N,a,b)$ denote the number of numbers not greater than N and divisible by at least one number between $a$ and $b$(inclusive).

For example, $P(15,3,5)=9$

3 can divide 3,6,9,12,15

4 can divide 4,8,12

5 can divide 5,10,15

There are 9 numbers not greater than 15 and divisible by at least one number between 3 and 5, namely 3,4,5,6,8,9,10,12,15.

You are given $P({10}^8,21,40)=41982923$

Find $P({10}^{17},61,120)$