module Lib
  ( factors,
    fib,
    primes,
    primeFactors,
    sumOfDigits,
  )
where

import Data.List (nub)

factors :: Integral a => a -> [a]
factors n = concat [if mod n f == 0 then nub [f, div n f] else [] | f <- [1 .. flsqrt n]]

fib :: [Integer]
fib = 1 : 2 : zipWith (+) fib (tail fib)

flsqrt :: Integral a => a -> a
flsqrt n = floor $ sqrt $ fromIntegral n

isPrime :: Integral a => a -> Bool
isPrime n = n > 1 && null [[] | k <- [2 .. flsqrt n], mod n k == 0]

primes :: [Integer]
primes = 2 : filter isPrime [3, 4 ..]

primeFactors :: Integral a => a -> [a]
primeFactors n = genPrimeFactors n 2
  where
    genPrimeFactors :: Integral a => a -> a -> [a]
    genPrimeFactors n c
      | c * c > n = [n]
      | mod n c /= 0 = genPrimeFactors n (c + 1)
      | otherwise = c : genPrimeFactors (div n c) c

sumOfDigits :: Integral a => a -> a
sumOfDigits n
  | n == 0 = 0
  | otherwise = mod n 10 + sumOfDigits (div n 10)