Dhaka Regional- 2017 Problem Name- Divisors

Revision en2, by Sukarna_Paul, 2018-11-15 10:05:32

How can I approach for this problem ?

8085 Divisors (Link)

The number of divisor function or d(n) is a very interesting function in number theory. It denotes the number of positive divisors of a particular number. For example d(24) = 8 as 24 has eight divisors 1, 2, 3, 4, 6, 8, 12 and 24 . In mathematics factorial of a positive integer number n is written as n! and is defined as below: n! = 1 × 2 × 3 × · · · × n

Another interesting function AF(n) (Again factorial in short) is defined as: AF(n) = 1! × 2! × 3! × . . . × n!

Given n , your job is to find the value of d(AF(n)).

Input The input file contains at most 101 lines of inputs. Each line contains an integer n (0 < n < 5000001) . Input is terminated by a line containing a single zero. This value should not be processed.

Output For each line of input produce one line of output.

This line contains the modulo 100000007 (10^8 + 7) of d(AF(n)).

Sample Input 1 2 3 4 100 0

Sample Output 1 2 6 18 59417661

Tags #number theory, divisors, factorial

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  Rev. Lang. By When Δ Comment
en2 English Sukarna_Paul 2018-11-15 10:05:32 2 Tiny change: '000007 (10 + 7) of d' -> '000007 (10^8 + 7) of d'
en1 English Sukarna_Paul 2018-11-15 10:04:31 1200 Initial revision (published)