Buddy Pairs - py

Python/5kyu/buddy_pairs.py

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+# https://www.codewars.com/kata/59ccf051dcc4050f7800008f
+# DESCRIPTION:
+# Buddy pairs
+# You know what divisors of a number are. The divisors of 
+# a positive integer n are said to be proper when you 
+# consider only the divisors other than n itself. In the 
+# following description, divisors will mean proper divisors. 
+# For example for 100 they are 1, 2, 4, 5, 10, 20, 25, and 
+# 50.
+# Let s(n) be the sum of these proper divisors of n. Call 
+# buddy two positive integers such that the sum of the 
+# proper divisors of each number is one more than the other 
+# number:
+# (n, m) are a pair of buddy if s(m) = n + 1 and s(n) = m + 1
+# For example 48 & 75 is such a pair:
+#     Divisors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24 --> sum: 76 = 75 + 1
+#     Divisors of 75 are: 1, 3, 5, 15, 25 --> sum: 49 = 48 + 1
+# Task
+# Given two positive integers start and limit, the function 
+# buddy(start, limit) should return the first pair (n m) of 
+# buddy pairs such that n (positive integer) is between start 
+# (inclusive) and limit (inclusive); m can be greater than limit 
+# and has to be greater than n
+# If there is no buddy pair satisfying the conditions, then return 
+# "Nothing" or (for Go lang) nil or (for Dart) null; (for Lua, 
+# Pascal, Perl, D) [-1, -1]; (for Erlang {-1, -1}).
+# Examples
+#     (depending on the languages)
+#     buddy(10, 50) returns [48, 75] 
+#     buddy(48, 50) returns [48, 75]
+#     or
+#     buddy(10, 50) returns "(48 75)"
+#     buddy(48, 50) returns "(48 75)"
+# Notes
+#     for C: The returned string will be free'd.
+#     See more examples in "Sample Tests:" of your language.
+
+def divisors(num):
+    divs = {1}
+    for div in range(2, int(num**0.5) + 1):
+        if num % div == 0:
+            divs.add(div)
+            divs.add(int(num/div))
+    return divs
+
+def buddy(start, limit):
+    for x in range(start, limit + 1):
+        divs = sorted(divisors(x))
+        m = sum(divs) - 1
+        m_divs = divisors(m)
+        if x == sum(sorted(m_divs)) - 1 and m == sum(divs) - 1 and x < m: 
+            return [x, m]
+    return "Nothing"