{"code":"aicprtsp2","name":"An interesting counting problem related to square product 2","description":"Given $n (1 \\leq n \\leq 10^6)$, count the number of pairs $(a, b)$ that satisfies:\r\n\r\n- $1 \\leq a < b \\leq n$.\r\n- $a \\times b$ is a perfect square.\r\n\r\nSince the result can be large, output it under modulo $10^9 + 7$.\r\n\r\n<h4>Example</h4>\r\n\r\n!!! question \"Test 1\"\r\n\r\n    ???+ \"Input\"\r\n\r\n        ```sample\r\n        1\r\n        ```\r\n\r\n    ???+ success \"Output\"\r\n\r\n        ```sample\r\n        0\r\n        ```\r\n    \r\n    ??? warning \"Note\"\r\n        There are no satisfied integer pair $(a, b)$ that $1 \\leq a < b \\leq 1$.\r\n\r\n!!! question \"Test 2\"\r\n\r\n    ???+ \"Input\"\r\n\r\n        ```sample\r\n        10\r\n        ```\r\n\r\n    ???+ success \"Output\"\r\n\r\n        ```sample\r\n        4\r\n        ```\r\n    ??? warning \"Note\"\r\n        There are $4$ satisfied pairs: {$1, 4$}, {$1, 9$}, {$2, 8$}, {$4, 9$}.\r\n\r\n!!! question \"Test 3\"\r\n\r\n    ???+ \"Input\"\r\n\r\n        ```sample\r\n        25\r\n        ```\r\n\r\n    ???+ success \"Output\"\r\n\r\n        ```sample\r\n        16\r\n        ```\r\n    ??? warning \"Note\"  \r\n        There are $16$ satisfied pairs: {$1, 4$}, {$1, 9$}, {$1, 16$}, {$1, 25$}, {$2, 8$}, {$2, 18$}, {$3, 12$}, {$4, 9$}, {$4, 16$}, {$4, 25$}, {$5, 20$}, {$6, 24$}, {$8, 18$}, {$9, 16$}, {$9, 25$}, {$16, 25$}.","points":300.0,"partial":true,"time_limit":1.0,"memory_limit":1048576,"short_circuit":false,"allowed_languages":[3,4,34,36,37,5,6,11,12,14,28,2,38,39,9,18,17,29,23,27,35,25,26,10,7,19,32,1,8,15,16,24,20,33,13,41,21,40],"is_public":true,"is_manually_managed":false,"permissions":{"can_edit":false}}