Refactoring

src/Julia/Problems001-050/Problem021.jl

@@ -8,18 +8,40 @@ Solution for Problem 21 of Project Euler
 https://projecteuler.net/problem=21 =#
 
 using BenchmarkTools
+using Primes
 
-function divisors(n)
-    divisors = Int64[1]
-    m = round(Int, n / 2)
-    for i in 2:m
-        if n % i == 0
-            push!(divisors, i)
+
+function sum_divisors(n)
+    counter = 1
+    factors = factor(n)
+    factors_keys = keys(factors)
+
+    for i in factors_keys
+        count = 1
+        for j = 1:factors[i]
+            count += i^j
         end
+        counter *= count
     end
-    return divisors
+
+    return counter - n
 end
 
+function is_amicable(n)
+    s = sum_divisors(n)
+    if s == n
+        return false
+    end
+
+    sum_s = sum_divisors(s)
+    if sum_s == n
+        return true
+    end
+
+    return false
+end
+
+
 function Problem21()
     #=
     Let d(n) be defined as the sum of proper divisors of n (numbers
@@ -33,20 +55,14 @@ function Problem21()
 
     Evaluate the sum of all the amicable numbers under 10000 =#
 
-    n = 9999
-    s = zeros(Int, n)
-    amicable = Int64[]
-    for i in 2:n
-        s[i] = sum(divisors(i))
-    end
-
-    for i in 2:n
-        if s[i] <= n && i != s[i] && i == s[s[i]]
-            push!(amicable, i)
+    counter = 0
+    for i = 2:10_000
+        if is_amicable(i)
+            counter += i
         end
     end
 
-    return sum(amicable)
+    return counter
 end