Divide Both

AtCoder

IDabc206_e

Time2000ms

Memory256MB

Difficulty—

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: $L$ $R$ [samples]

Samples

Input #1

3 7

Output #1

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: $(x,y)=(4,6),(6,4)$.

Input #2

4 10

Output #2

Input #3

1 1000000

Output #3

392047955148

API Response (JSON)

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    "name": "Divide Both",
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      "content": "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 $x$ a",
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      "statement_type": "Markdown",
      "content": "Given integers $L$ and $L,R\\ (L \\le R)$, find the number of pairs $(x,y)$ of integers satisfying all of the conditions below:\n\n*   $L \\le x,y \\le R$\n*   Let $g$ be the greatest common divisor of $x$ a...",
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