{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eA square-free integer is an integer which is indivisible by any square number except $1$. For example, $6 \u003d 2 \\cdot 3$ is square-free, but $12 \u003d 2^2 \\cdot 3$ is not, because $2^2$ is a square number. Some integers could be decomposed into product of two square-free integers, there may be more than one decomposition ways. For example, $6 \u003d 1\\cdot 6\u003d6 \\cdot 1\u003d2\\cdot 3\u003d3\\cdot 2, n\u003dab$ and $n\u003dba$ are considered different if $a \\not \u003d b$. $f(n)$ is the number of decomposition ways that $n\u003dab$ such that $a$ and $b$ are square-free integers. The problem is calculating $\\sum_{i \u003d 1}^nf(i)$.\u003c/p\u003e\u003ch3\u003eInput\u003c/h3\u003e\u003cp\u003eThe first line contains an integer $T(T\\le 20)$, denoting the number of test cases. \u003c/p\u003e\u003cp\u003eFor each test case, there first line has a integer $n(n \\le 2\\cdot 10^7)$.\u003c/p\u003e\u003ch3\u003eOutput\u003c/h3\u003e\u003cp\u003eFor each test case, print the answer $\\sum_{i \u003d 1}^n f(i)$.\u003c/p\u003e\u003ch3\u003eHint\u003c/h3\u003e\u003cp\u003e$\\sum_{i \u003d 1}^8 f(i)\u003df(1)+ \\cdots +f(8)$\u003cbr\u003e$\u003d1+2+2+1+2+4+2+0\u003d14$.\u003c/p\u003e"}},{"title":"Sample 1","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2\n5\n8\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e8\n14\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cbr /\u003e"}}]}