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Task/Perfect-numbers/CoffeeScript/perfect-numbers.coffee

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+is_perfect_number = (n) ->
+  do_factors_add_up_to n, 2*n
+
+do_factors_add_up_to = (n, desired_sum) ->
+  # We mildly optimize here, by taking advantage of
+  # the fact that the sum_of_factors( (p^m) * x)
+  # is (1 + ... + p^m-1 + p^m) * sum_factors(x) when
+  # x is not itself a multiple of p.
+
+  p = smallest_prime_factor(n)
+  if p == n
+    return desired_sum == p + 1
+
+  # ok, now sum up all powers of p that
+  # divide n
+  sum_powers = 1
+  curr_power = 1
+  while n % p == 0
+    curr_power *= p
+    sum_powers += curr_power
+    n /= p
+
+  # if desired_sum does not divide sum_powers, we
+  # can short circuit quickly
+  return false unless desired_sum % sum_powers == 0
+
+  # otherwise, recurse
+  do_factors_add_up_to n, desired_sum / sum_powers
+
+smallest_prime_factor = (n) ->
+  for i in [2..n]
+    return n if i*i > n
+    return i if n % i == 0
+
+# tests
+do ->
+  # This is pretty fast...
+  for n in [2..100000]
+    console.log n if is_perfect_number n
+
+  # For big numbers, let's just sanity check the known ones.
+  known_perfects = [
+    33550336
+    8589869056
+    137438691328
+  ]
+  for n in known_perfects
+    throw Error("fail") unless is_perfect_number(n)
+    throw Error("fail") if is_perfect_number(n+1)