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: 2016-06-05 19:08:56

AC in first go! :D

azam_9: 2016-06-03 08:59:07

modified sieve also works..

katyalch: 2016-05-16 05:48:30

uh oh tle

manav_itmu: 2016-05-15 21:32:31

tle. any help ?

shubhanshu001: 2016-05-15 15:35:05

AC in first go!!..:)

mohitgupta07: 2016-05-08 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: 2016-04-24 15:43:14

@hrithik,vijay... calculate divisors up to sqrt(n) . For better runtime you can use modified sieve

hrithik_sethia: 2016-04-19 19:59:31

getting tle please how do we do this??

vijayreddie: 2016-03-24 06:12:37

time limit exceeded how to

pranjalikumar9: 2016-02-14 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:2004-06-10
Time limit:3s
Source limit:5000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:Neal Zane