Problem 337

Totient Stairstep Sequences

Let {a_{1}, a_{2},..., a_{n}} be an integer sequence of length `n` such that:

- a
_{1}= 6 - for all 1
`i`n : φ(a_{i})`i`+1)`i``i`+1^{1}

Let S(`N`) be the number of such sequences with a_{n}`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 10^{8} = 73808307.

Find S(20 000 000) mod 10^{8}.

^{1} φ denotes **Euler's totient function**.

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These problems are part of
Project Euler
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