E - Divide Both

Score : $500$ points

Problem Statement

Given integers $L$ and $L,R\ (L \le R)$, find the number of pairs $(x,y)$ of integers satisfying all of the conditions below:

• $L \le x,y \le R$
• Let $g$ be the greatest common divisor of $x$ and $y$. Then, the following holds.
  • $g \neq 1$, $\frac{x}{g} \neq 1$, and $\frac{y}{g} \neq 1$.

Constraints

• All values in input are integers.
• $1 \le L \le R \le 10^6$

Input

Input is given from Standard Input in the following format:

$L$ $R$

Output

Print the answer as an integer.

3 7

2

Let us take some number of pairs of integers, for example.

• $(x,y)=(4,6)$ satisfies the conditions.
• $(x,y)=(7,5)$ has $g=1$ and thus violates the condition.
• $(x,y)=(6,3)$ has $\frac{y}{g}=1$ and thus violates the condition.

There are two pairs satisfying the conditions: $(x,y)=(4,6),(6,4)$.

4 10

12

1 1000000

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