Project euler69 #1510

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	/**
	// https://projecteuler.net/problem=69

	Euler's totient function, phi(n) [sometimes called the phi function], is defined
	as the number of positive integers not exceeding n which are relatively prime to n.
	For example, as 1, 2, 4, 7, 8, are all less than or equal to nine
	and relatively prime to nine, phi(9)=6.

	It can be seen that n=6 produces a maximum n/phi(n) for n <= 10

	Find the value of n <= 1000000 for which n/phi(n) is a maximum.

	*/
	export const answer = (maxVal) => {
	//To minimize n/phi(n), phi(n) must have the most unique prime factors, n must be equal to the product of primes each to the first power, so it equals to 2357...
	var productSoFar = 1;
	var primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,57];
	for (var idx=0;idx<primes.length;idx++){
	if (productSoFar*primes[idx] > maxVal){
	return productSoFar;
	}
	productSoFar *= primes[idx];
	}
	}

12 changes: 12 additions & 0 deletions Project-Euler/test/Problem069.test.js

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	import { answer } from '../Problem069.js'

	describe('maximizing n/phi(n)', () => {
	// Project Euler Condition Check
	test('Maximum value for n <= 1000', () => {
	expect(answer(1000)).toBe(210)
	})
	// Project Euler Second Value for Condition Check
	test('Maximum value for n <= 123456789', () => {
	expect(answer(123456789)).toBe(9699690)
	})
	})

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