2.0 KiB

Raw Blame History

id	title	challengeType	forumTopicId	dashedName
5900f3b11000cf542c50fec4	Problem 69: Totient maximum	5	302181	problem-69-totient-maximum

--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.

!!crwdBlockTags_15_sgaTkcolBdwrc!!	Relatively Prime	φ(!!crwdBlockTags_16_sgaTkcolBdwrc!!)	!!crwdBlockTags_17_sgaTkcolBdwrc!!/φ(!!crwdBlockTags_18_sgaTkcolBdwrc!!)
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.

--hints--

totientMaximum() should return a number.

assert(typeof totientMaximum() === 'number');

totientMaximum() should return 510510.

assert.strictEqual(totientMaximum(), 510510);

--seed--

--seed-contents--

function totientMaximum() {

  return true;
}

totientMaximum();

--solutions--

// solution required

2.0 KiB Raw Blame History