# Problem 337: Totient Stairstep Sequences

![graphic](img337.gif)

Let {a1, a2,..., an} be an integer sequence of length n such that: a1 =
6 for all 1 ≤ i < n : φ(ai) < φ(ai+1) < ai < ai+11 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.