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import { aliquotSum } from '../Maths/AliquotSum.js'

/**

* Problem 21 - Amicable numbers

* @see {@link https://projecteuler.net/problem=21}

* Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).

* If d(a) = b and d(b) = a, where a != b, then a and b are an amicable pair and each of a and b are called amicable numbers.

* For example, the proper divisors of 220 are 1,2,4,5,10,11,20,22,44,55 and 110; therefore d(220) = 284.

* The proper divisors of 284 are 1,2,4,71 and 142; so d(284) = 220.

* Evaluate the sum of all amicable numbers under 10000

* @author PraneethJain

function problem21(n) {

if (n < 2) {

throw new Error('Invalid Input')

}

let result = 0

for (let a = 2; a < n; ++a) {

const b = aliquotSum(a) // Sum of all proper divisors of a

// Check if b > a to ensure each pair isn't counted twice, and check if sum of proper divisors of b is equal to a

if (b > a && aliquotSum(b) === a) {

result += a + b

}

return result

}

export { problem21 }