A positive integer is perfect if it equals the sum of all of its factors, excluding the number i

step 1 For this one, we're looking for perfect numbers. And so when I get my perfect numbers, I'm going

A positive integer is perfect if it equals the sum of all of...

Key Concepts

Factors Function

A factors function is used to determine all divisors of a given integer. It is fundamental in the context of perfect numbers as it helps in identifying the proper divisors whose sum is compared with the original number to ascertain its perfection.

Type Signatures in Haskell

Type signatures in Haskell explicitly declare the types of a function’s inputs and outputs, ensuring clarity and type safety. For example, a function with signature Int -> [Int] indicates that it takes an integer and returns a list of integers.

List Comprehension in Functional Programming

List comprehensions provide a succinct way to generate lists by filtering and transforming existing lists based on specified conditions. In languages like Haskell, they offer an elegant syntax for iterating over collections and building new lists.

Perfect Numbers

A perfect number is a positive integer that equals the sum of its proper divisors, which are the factors of a number excluding the number itself. This concept is significant in number theory and is used to study the properties and classifications of numbers.

Transcript

00:01 For this one, we're looking for perfect numbers.

00:04 And so when i get my perfect numbers, i'm going to store them in a string.

00:10 And actually, i'm not going to store them in a string.

00:12 I'm going to store them in a list.

00:13 And so i'm going to make my list with all of my perfect numbers.

00:18 We're told that we have four of them between or less than 10 ,000.

00:24 So there's probably nice ways to do optimization to make this go quicker.

00:28 I'm going to do some serious brute force in this program.

00:35 I'm going to test every number from 1 to 10 ,000, and so i'm going to type in 10 ,0001 for my range.

00:45 And so for each one of those, i'm going to look for the, to see if any of those are perfect numbers.

00:54 I'm going to say that my number is equal to my value, value and i don't need to do that.

01:05 When i originally wrote that, i was thinking we were going to be factoring the number and we're doing something slightly different.

01:12 I'm going to use the word divisors because i want to find all the number.

01:19 When i've like 14, i want to find all the numbers that equally divide into 14, which be one, two, seven, and 14.

01:29 So divisors, i'm going to build a list.

01:31 Nope, i'm going to build a list.

01:33 Of my divisors and then i'm going to start off saying for factor could call that divisor in range one to value and actually my example earlier i would not want to use 14 as one of the divisors okay so we want to test to see if the factor is evenly divisible by or evenly divides the numbers i'm going to say the number when i divide the number by factor, if i get a zero, i know that the number is an integer divisor, and then i'm gonna say divisors dot append, and i'm gonna add the number.

02:43 Actually, it's called a factor.

02:44 I'm gonna add the factor to the list.

02:49 When i get done with that, so for each of those numbers, when i get my list of divisors, i'm going to get my, i'm going to create a variable called factor sum.

03:04 I'm going to call that equal to zero and four.

03:09 You could call it divisor.

03:11 I'm just going to call it item.

03:12 For item in divisors.

03:17 Divisors.

03:19 So i'm going to go through each of the divisors.

03:21 So one, two, and seven for 14.

03:26 And i'm going to increment factor sum.

03:33 By the value of that divisor value...