primes = (2 : filter (check primes) [3..]) where
    check (p:ps) n | p*p > n = True
                   | n `mod` p == 0 = False
                   | otherwise = check ps n
 
sumDiv n = (divs n primes) - n where
    divs 1 _ = 1
    divs n (p:ps) =
        if p*p > n
            then n+1
            else let (c, r) = cnt n p 0 in
                if c == 0
                    then divs n ps
                    else (sum $ take (c+1) $ iterate (*p) 1) * (divs r ps)
    cnt n p c | mod n p == 0 = cnt (div n p) p (c+1)
              | otherwise = (c, n)
 
friends :: [(Integer, Integer)]
friends = filter (\(x, s) -> x < s && sumDiv s == x) $ map (\x -> (x, sumDiv x)) [1..]
 
main = mapM print $ take 37 friends

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