{"trustable":true,"sections":[{"title":"","value":{"format":"MD","content":"We all know that any integer number **n** is divisible by **1** and **n**. That is why these two numbers are not the actual divisors of any numbers. The function **SOD(n)** (sum of divisors) is defined as the summation of all the actual divisors of an integer number **n**. For example, **SOD(24) \u003d 2+3+4+6+8+12 \u003d 35**.\n\nThe function **CSOD(n)** (cumulative **SOD**) of aninteger **n**, is defined as below:\n\n$$CSOD(n) \u003d \\sum_{i\u003d1}^nSOD(i)$$\n\nGiven the value of **n**, your job is to find the value of **CSOD(n)**."}},{"title":"Input","value":{"format":"MD","content":"Input starts with an integer **T (\u0026#8804; 1000)**, denoting the number of test cases.\n\nEach case contains an integer **n (0 \u0026#8804; n \u0026#8804; 2 \\* 10\u003csup\u003e9\u003c/sup\u003e)**."}},{"title":"Output","value":{"format":"MD","content":"For each case, print the case number and the result. You may assume that each output will fit into a **64** bit signed integer."}},{"title":"Sample","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\u003e3\n2\n100\n200000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase 1: 0\nCase 2: 3150\nCase 3: 12898681201837053\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}