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:All
Resource:Neal Zane

hide comments
2018-11-09 06:39:39
i get time limit exceed in python
2018-10-31 17:31:25
1 should be output 0
OMFG I have checked it for hours.
2018-09-24 17:40:51
AC in one go!!!!meow bheow kakkaw raar!!!!
2018-08-27 10:19:56
AC in ONE GO !!!

Last edit: 2018-08-27 10:21:16
2018-08-18 18:30:01
Do you have any test case?

In PHP, I still get wrong answer.

Please see my solution at: <snip>

Last edit: 2023-03-08 17:56:03
2018-05-12 17:41:48
Super easy
waste of time ('_')
2018-04-19 06:30:30
why its time limit exceeded?
2018-03-29 09:02:46
the answer for 1 should be 0. It costs me two wrong answers. :(
2018-02-06 13:07:54
AC in ONE GO !!!

Last edit: 2018-02-06 13:08:23
2018-01-13 13:08:11
a nyc problem
the simple logic is that we loop around for i*i<n
think simple logic dont bother about learning sieve

Last edit: 2018-01-13 13:09:03
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