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// https://projecteuler.net/problem=1

/* Multiples of 3 and 5

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6, and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below the provided parameter value number.

*/

// This method uses the nSum function to add the nSum for 3 and 5. However, it needs to subtract the nSum for 15 once to avoid double counting.

const multiplesThreeAndFive = (num) => {

if (num < 1) throw new Error('No natural numbers exist below 1')

num -= 1

let sum = 0

// The nSum function calculates the sum of the first n numbers in the sequence with a common difference of num.

// Here, n is denoted as frequency.

const nSum = (num, frequency) => (frequency * (frequency + 1) * num) >> 1

sum += nSum(3, Math.floor(num / 3))

sum += nSum(5, Math.floor(num / 5))

sum -= nSum(15, Math.floor(num / 15))

return sum

}

export { multiplesThreeAndFive }