942 B
942 B
id | title | challengeType | forumTopicId |
---|---|---|---|
5900f4421000cf542c50ff55 | Problem 214: Totient Chains | 5 | 301856 |
--description--
Let φ be Euler's totient function, i.e. for a natural number n,
φ(n) is the number of k, 1 ≤ k ≤ n, for which gcd(k,n) = 1.
By iterating φ, each positive integer generates a decreasing chain of numbers ending in 1. E.g. if we start with 5 the sequence 5,4,2,1 is generated. Here is a listing of all chains with length 4:
5,4,2,1 7,6,2,1 8,4,2,1 9,6,2,1 10,4,2,1 12,4,2,1 14,6,2,1 18,6,2,1
Only two of these chains start with a prime, their sum is 12.
What is the sum of all primes less than 40000000 which generate a chain of length 25?
--hints--
euler214()
should return 1677366278943.
assert.strictEqual(euler214(), 1677366278943);
--seed--
--seed-contents--
function euler214() {
return true;
}
euler214();
--solutions--
// solution required