SPOJ Problem Set (classical)

1754. Divisor Summation (Hard)

Given a natural number n (1 <= n <= 1e16), 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.

An integer stating the number of test cases (equal to 500), and that many lines follow, each containing one integer between 1 and 1e16 inclusive.

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

Input:
3
2
10
20

Output:
1
8
22

warning: a naive algorithm may not run in time.

Added by:	Jin Bin
Date:	2007-08-29
Time limit:	60s
Source limit:	50000B
Languages:	All except: C99 strict ERL TECS JS
Resource:	own problem


2010-03-14 05:00:53 abhijith reddy d +1 My code factors random 500 numbers in < 0.5 secs on my computer .. here it takes 8 secs .. and also so many overflows !! Last edit: 2010-03-14 05:01:10
2010-03-02 23:54:29 Nic Roets Just to make it clear: The 500 test numbers were not randomly chosen. They were chosen to make the run time as long as possible.