Syntax error Program to find out the sum of the number of divisor of the divisors in Python

Program to find out the sum of the number of divisor of the divisors in Python

Suppose we are given two integer numbers m and a. Now n = p1(a + 1) *p2(a + 2) *...*pm(a + m), where pi is the i-th prime number and i > 0. We have to find the value of k, where k = summation of f(x) values of n. Here f(x) values are the number of divisor values of each divisor of n.

So, if the input is like m = 2, a = 1, then the output will be 60.

  • So, n = 2^2 x 3^3
  • n = 4 x 27
  • n = 108

The divisors of 108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

f(x) value of each divisor are: f(1) + f(2) + f(3) + f(4) + f(6) + f(9) + f(12) + f(18) + f(27) + f(36) + f(54) + f(108)

= 1 + 2 + 2 + 4 + 4 + 3 + 5 + 6 + 4 + 9 + 8 + 12

= 60.

To solve this, we will follow these steps −

  • MOD := 10^9 + 7
  • Define a function summ() . This will take n
    • return floor value of ((n * (n + 1)) / 2)
  • Define a function division() . This will take a, b, mod
    • if a mod b is same as 0, then
      • return floor value of a / b
    • a := a + mod * division((-a modulo b), (mod modulo b), b)
    • return floor value of (a / b) modulo mod
  • mat := a new list containing a value 1
  • while size of mat <= m + a, do
    • insert (last element of mat * summ(len(mat)+1)) mod MOD at the end of mat
  • return division(mat[m + a], mat[a], MOD)

Example

Let us see the following implementation to get better understanding −

MOD = 10**9 + 7
def summ(n):
   return ((n) * (n + 1)) // 2

def division(a, b, mod):
   if a % b == 0:
      return a // b
   a += mod * division((-a) % b, mod % b, b)
   return (a // b) % mod

def solve(m, a):
   mat = [1]
   while len(mat) <= m + a:
      mat.append((mat[-1] * summ(len(mat)+1)) % MOD)
   return division(mat[m + a] , mat[a], MOD)

print(solve(2, 1))

Input

2, 1

Output

60
Updated on: 2021-10-20T08:00:18+05:30

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