Problem 337
Totient Stairstep Sequences

Let {a1, a2,..., an} be an integer sequence of length n such that:

  • a1 = 6
  • for all 1 ≤i n : φ(ai) i+1) i i+1 1

Let S(N) be the number of such sequences with an≤N.
For example, S(10) = 4: {6}, {6, 8}, {6, 8, 9} and {6, 10}.
We can verify that S(100) = 482073668 and S(10 000) mod 108 = 73808307.

Find S(20 000 000) mod 108.

1 φ denotes Euler's totient function.

These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK

http://projecteuler.net/problem=337