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## DIVSUM - Divisor Summation |

Given a natural number n (1 <= n <= 500000), please output the summation of all its proper divisors.

*Definition:* A proper divisor of a natural number is the divisor that is strictly less than the number.

e.g. number 20 has 5 proper divisors: 1, 2, 4, 5, 10, and the divisor summation is: 1 + 2 + 4 + 5 + 10 = 22.

### Input

An integer stating the number of test cases (equal to about 200000), and that many lines follow, each containing one integer between 1 and 500000 inclusive.

### Output

One integer each line: the divisor summation of the integer given respectively.

### Example

Sample Input: 3 2 10 20 Sample Output: 1 8 22

**Warning: large Input/Output data, be careful with certain languages**

Added by: | Neal Zane |

Date: | 2004-06-10 |

Time limit: | 3s |

Source limit: | 5000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | C-CLANG C C++ 4.3.2 CPP CPP14 CPP14-CLANG C99 JAVA PYTHON PYTHON3 SWIFT |

Resource: | Neal Zane |