[国家集训队] 和与积 - 题目详情 - 33OJ

ID: 5191

远端评测题

1000ms

250MiB

显示难度省选/NOI−

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2012

集训队互测

Problem Description

Given $n$ , count the number of pairs $(a, b)$ that satisfy the following conditions:

$1 \le a < b \le n$ .
$a + b$ divides $a \times b$ .

Input Format

One line containing an integer $n$ .

Output Format

One line containing an integer representing the answer.

Hint

Test	$N$	Test	$N$
$1$	$\leq 10$	$11$	$\leq 5\times 10^7$
$2$	$\leq 50$	$12$	$\leq 10^8$
$3$	$\leq 10^3$	$13$	$\leq 2\times 10^8$
$4$	$\leq 5\times 10^3$	$14$	$\leq 3\times 10^8$
$5$	$\leq 2\times 10^4$	$15$	$\leq 5\times 10^8$
$6$	$\leq 2\times 10^5$	$16$	$\leq 10^9$
$7$	$\leq 2\times 10^6$	$17$	$\leq 10^9$
$8$	$\leq 10^7$	$18$	$\leq 2^{31}-1$
$9$	$\leq 2\times 10^7$	$19$
$10$	$\leq 3\times 10^7$	$20$

Source: 2012 CTT mutual test, by ayq.

Translated by ChatGPT 5