#!/usr/bin/env stack
{- stack script
   --resolver lts-13.24
   --install-ghc
   --package arithmoi
-}

{-
Consider the fraction, n/d, where n and d are positive integers. If n<d and
HCF(n,d)=1, it is called a reduced proper fraction.

If we list the set of reduced proper fractions for d ≤ 8 in ascending order of
size, we get:

1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

It can be seen that there are 21 elements in this set.

How many elements would be contained in the set of reduced proper fractions for
d ≤ 1,000,000?
-}
{-# LANGUAGE NoImplicitPrelude #-}
import Protolude
import Math.NumberTheory.Primes

-- reducedProper :: Int -> [Int]
reducedProper d = do
  let pf = map fst $ factorise d
  x <- [1..d]
  guard (some (\p -> x `rem` p == 0) pf)
  return x

main :: IO ()
main = do
  print $ reducedProper 8