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Added a new Maths algorithm to determine if two non-null integers are "friendly numbers" #1267

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Merged
merged 3 commits into from
Nov 30, 2022
Merged

Added a new Maths algorithm to determine if two non-null integers are "friendly numbers" #1267

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a45e411
Added FriendlyNumbers.js, to determine if two integers are friendly n…
fun-guava Nov 27, 2022
27cf176
Fixed a typo in the error message
fun-guava Nov 27, 2022
7ce4bf3
Following the advice of appgurueu, outsourced abundancyIndex ot its o…
fun-guava Nov 27, 2022
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32 changes: 32 additions & 0 deletions Maths/FriendlyNumbers.js
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/*
'In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the
ratio between the sum of divisors of a number and the number itself.'
Source: https://en.wikipedia.org/wiki/Friendly_number
See also: https://mathworld.wolfram.com/FriendlyNumber.html#:~:text=The%20numbers%20known%20to%20be,numbers%20have%20a%20positive%20density.
*/

export const FriendlyNumbers = (firstNumber, secondNumber) => {
// input: two integers
// output: true if the two integers are friendly numbers, false if they are not friendly numbers

// First, check that the parameters are valid
if (!Number.isInteger(firstNumber) || !Number.isInteger(secondNumber) || firstNumber === 0 || secondNumber === 0 || firstNumber === secondNumber) {
throw new Error('The two parameters must be distinct, non-null integers')
}

return abundancyIndex(firstNumber) === abundancyIndex(secondNumber)
}

function abundancyIndex (number) {
return sumDivisors(number) / number
}

function sumDivisors (number) {
let runningSumDivisors = number
for (let i = 0; i < number / 2; i++) {
if (Number.isInteger(number / i)) {
runningSumDivisors += i
}
}
return runningSumDivisors
}