yaworsw/euler-manager

---
:id: 214
:name: Totient Chains
:url: https://projecteuler.net/problem=214
:content: "Let φ be Euler's totient function, i.e. for a natural number <var>n</var>,
  φ(<var>n</var>) is the number of <var>k</var>, 1 ≤ <var>k</var> ≤ <var>n</var>,
  for which gcd(<var>k</var>,<var>n</var>) = 1.\n\nBy iterating φ, each positive integer
  generates a decreasing chain of numbers ending in 1.  \nE.g. if we start with 5
  the sequence 5,4,2,1 is generated.  \nHere is a listing of all chains with length
  4:\n\n5,4,2,1  \n7,6,2,1  \n8,4,2,1  \n9,6,2,1  \n10,4,2,1  \n12,4,2,1  \n14,6,2,1
  \ \n18,6,2,1\n\nOnly two of these chains start with a prime, their sum is 12.\n\nWhat
  is the sum of all primes less than 40000000 which generate a chain of length 25?\n\n"