What is the sum of the divisors of N?

In general, if you have the prime factorization of the number n, then to calculate the sum of its divisors, you take each different prime factor and add together all its powers up to the one that appears in the prime factorization, and then multiply all these sums together! Example: Determine S(1800).

What numbers are divisors of 4?

Example: 4 has for divisors 2 and 1. And 2+1=3 inferior to 4, so 4 is a deficient number. Example: The first deficient numbers are: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50…

How do you find the perfect 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.

What is the number of divisors of N?

Let d( n ) be the number of divisors for the natural number, n . We begin by writing the number as a product of prime factors: n = p a q b r c then the number of divisors, d( n ) = ( a +1)( b +1)( c +1)… To prove this, we first consider numbers of the form, n = p a .

What are perfect divisors?

Perfect divisors are those divisors which are square of some integer. For example a perfect divisor of 8 is 4.

What are the divisors of 220?

They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220. (A proper divisor of a number is a positive factor of that number other than the number itself.

What is a perfect power of a number?

A perfect power is a number that can be expressed as power of another positive integer. Given a number n, find count of numbers from 1 to n that are of type x y where x >= 1 and y > 1. Examples : Input : n = 10 Output : 4 1 4 8 and 9 are the numbers that are of form x ^ y where x > 0 and y > 1 Input : n = 50 Output : 10.

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. Examples :

What is the formula for a perfect number n?

A Perfect Number “n”, is a positive integer which is equal to the sum of its factors, excluding “n” itself. Euclid, over two thousand years ago, showed that all even perfect numbers can be represented by, N = 2p-1(2p -1) where p is a prime for which 2p -1 is a Mersenne prime.

How to check if a number is a perfect number?

A number is a perfect number if is equal to sum of its proper divisors, that is, sum of its positive divisors excluding the number itself. Write a function to check if a given number is perfect or not. Examples: Input: n = 15 Output: false Divisors of 15 are 1, 3 and 5. Sum of divisors is 9 which is not equal to 15.