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id	challengeType	title	forumTopicId
5900f3b11000cf542c50fec4	5	Problem 69: Totient maximum	302181

Description

Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of numbers less than n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6.

n Relatively Prime φ(n) n/φ(n) 2 1 1 2 3 1,2 2 1.5 4 1,3 2 2 5 1,2,3,4 4 1.25 6 1,5 2 3 7 1,2,3,4,5,6 6 1.1666... 8 1,3,5,7 4 2 9 1,2,4,5,7,8 6 1.5 10 1,3,7,9 4 2.5

It can be seen that n=6 produces a maximum n/φ(n) for n ≤ 10. Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.

Instructions

Tests

tests:
  - text: <code>euler69()</code> should return 510510.
    testString: assert.strictEqual(euler69(), 510510);

Challenge Seed

function euler69() {
  // Good luck!
  return true;
}

euler69();

Solution

// solution required

1.2 KiB Raw Blame History