Question

a positive integer is nice if there is a positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to . how many numbers in the set are nice?

Answer 1

Answer:

A positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to The sum of four divisors is equal to 45360.

What is an integer?

Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The inverses of the equivalent positive numbers, which are additive, are the negative numbers. The boldface Z or blackboard bold "Z" is frequently used in mathematical notation to represent a collection of numbers.

Step-by-step explanation:

We know That total No. of factors

=product of (prime no′s power+1)

If N is the number of different divisors:

N=(p1​+1)⋅(p2​+1)⋅⋅⋅(pn​+1)

100= 2^2 × 5^2

=2×2×5×5= (1+1)(1+1)(4+1)(4+1)

Then the integer n=  a1^p1​​⋅a2^p2​​⋅⋅⋅⋅an^pn​​

For the smallest value: p1​=4,p2​=4,p3​=1,p4​=1

Then,

n=a1^4​×a2^4​×a3^1​×a4^1​

=24⋅34⋅51⋅71

=16⋅81⋅5⋅7

=45360

Hence, the positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to The sum of four divisors is equal to 45360.

To learn more about the integers from the given link

brainly.com/question/929808

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