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
hide comments
visvats_141095:
20160605 19:08:56
AC in first go! :D 

azam_9:
20160603 08:59:07
modified sieve also works.. 

katyalch:
20160516 05:48:30
uh oh tle 

manav_itmu:
20160515 21:32:31
tle. any help ? 

shubhanshu001:
20160515 15:35:05
AC in first go!!..:) 

mohitgupta07:
20160508 21:12:56
yeah...simple maths..:) :) feeling gud after doing it wid just 1 try(actually got 1 wa coz of that n=1 )..yeah :D 

shanti_chai:
20160424 15:43:14
@hrithik,vijay... calculate divisors up to sqrt(n) . For better runtime you can use modified sieve 

hrithik_sethia:
20160419 19:59:31
getting tle please how do we do this?? 

vijayreddie:
20160324 06:12:37
time limit exceeded how to 

pranjalikumar9:
20160214 18:27:14
Just need to know that divisors exist in pairs. If i divides n then n/i also divides n. And smaller of the 2 divisors lies below sqrt(n) 
Added by:  Neal Zane 
Date:  20040610 
Time limit:  3s 
Source limit:  5000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  Neal Zane 