module _69

open common

let relativePrimeFunc =

    let primeDivisorArrayByMax max =
        let isPrime = isPrimeFunByMax (int (System.Math.Ceiling(sqrt (float max))))
        divisorsInclSelf max |> Array.map (List.filter isPrime)

    let totientArrayByMax max =
        let pd = primeDivisorArrayByMax max
        let productFormula n primes =
            let pFunc prime = 1.0 - 1.0/(float prime)
            primes 
            |> List.fold (fun p prime -> p * (pFunc prime)) (float n)
        pd
        |> Array.mapi productFormula
    
    let indexArray = Array.mapi (fun i e -> (i,e))

    totientArrayByMax 1000000
    |> indexArray
    |> Seq.skip 1
    |> Seq.map (fun (i,t) -> (i, (float i)/t))
    |> Seq.maxBy snd