How do you find the sum of the proper divisors of a number?
∑ d ∣ n d = ∏ i = 1 k p i m i + 1 – 1 p i – 1 . If we want only proper divisors, we should not include n in the sum, so we obtain the formula for proper divisors by subtracting n from our formula. (24−12−1)(33−13−1)(53−15−1)=15⋅26⋅1242⋅4=6045….Proof.
| Title | formula for sum of divisors |
|---|---|
| Classification | msc 11A05 |
What is the sum of all the divisors?
The formula for finding the sum of divisors is given as: Sum of divisors =(P0+P1+P2…… Pa)(q0+q1+q2……qb)(r0+r1+r2…… rc) .
What is proper divisor?
A positive proper divisor is a positive divisor of a number , excluding itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not. The number of proper divisors of is therefore given by. where is the divisor function.
How do you find the sum of the divisors of 8064?
The sum of these divisors (counting 8,064) is 26,520, the average is 55,2.5….Divisors of 8064.
| Even divisors | 42 |
|---|---|
| 4k+3 divisors | 3 |
What is the sum of divisors of 360?
Solution : The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. ∴ the sum of all odd proper divisors of 360 is 78.
How do you find the sum of the divisors of a number in Python?
Python Math: Returns sum of all divisors of a number
- Sample Solution:-
- Python Code: def sum_div(number): divisors = [1] for i in range(2, number): if (number % i)==0: divisors.append(i) return sum(divisors) print(sum_div(8)) print(sum_div(12))
- Pictorial Presentation:
- Flowchart:
- Python Code Editor:
How do you find the number of divisors of 1420?
1420 contains number of terms = 3 × 2 × 2 = 12; Then, the number of factors or divisors = 12.
What is the sum of divisors of 18?
39
Hence, the sum of the divisors of 18 is 39.
What are the proper divisors of 60?
1 to 100
| n | Divisors | σ(n) |
|---|---|---|
| 59 | 1, 59 | 60 |
| 60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 | 168 |
| n | Divisors | σ(n) |
| 61 | 1, 61 | 62 |
What are the proper divisors of 12?
Example: 12 has for divisors 6, 4, 3, 2 and 1.
What is the sum of all divisors of 133?
The number 133 can be divided by 4 positive divisors (out of which 0 are even, and 4 are odd). The sum of these divisors (counting 133) is 160, the average is 40.
What is the sum of all proper divisors of a number?
Given a natural number, calculate sum of all its proper divisors. A proper divisor of a natural number is the divisor that is strictly less than the number. For example, number 20 has 5 proper divisors: 1, 2, 4, 5, 10, and the divisor summation is: 1 + 2 + 4 + 5 + 10 = 22. Attention reader! Don’t stop learning now.
How do you find the sum of divisors of nequals?
Theorem 1. Suppose that nis a positive integerwhose factorization into prime factorsis ∏i=1kpimi, where the pi’s are distinct primes and the multiplicitiesmiare all at least 1. Then the sum of the divisors of nequals
How do you find all the divisors of N?
All the divisors of n can be expressed as p 1a x p 2b x …, where 0 <= a <= k1 and 0 <= b <= k2. (p 10 x p 2k2) + (p 11 x p 2k2) +……+ (p 1k1 x p 2k2 ).
How do you find the sum of all divisors of an array?
So, given a number n, by prime factorization we can find the sum of divisors of all the divisors. But in this problem we are given that n is product of element of array. So, find prime factorization of each element and by using the fact a b x a c = a b+c.