Various old cultures searched a connection between a number and the sum of its positive divisors. Numbers with special properties were often given a mystical interpretation. Positive integers that are equal to the sum of their positive divisors are called perfect numbers. Here, 1 is seen as a positive denominator of every number, and a number is not seen as a positive divisor of itself. Like that, the ancient Greeks already knew the first four positive divisors (see the table underneath), and currently there are 44 positive divisors.

Integers of which the sum of the positive divisors is smaller than the number itself are called deficient numbers, and integers of which the sum of their positive divisors is larger than the number itself are called abundant numbers.

Assignment

1. Write a function sum_divisors, that prints the sum of the positive divisors of a given integer (that is given to the function as a parameter). This way, for the value $$9$$, the function should print the result $$4$$ (= $$1 + 3$$), and the value $$10$$ results in the sum $$8$$ (= $$1 + 2 + 5$$).

   def sum_divisors(n)

2. Use the function sum_divisors to write a function kindofnumber, that prints a string for a given integer that indicates the kind of number: perfect, deficient or abundant. That way, the function should print perfect for the value $$28$$.

   def kindofnumber(n)

Example

>>> sum_divisors(28)
28
>>> kindofnumber(28)
'perfect'
>>> sum_divisors(29)
1
>>> kindofnumber(29)
'deficient'
>>> sum_divisors(30)
42
>>> kindofnumber(30)
'abundant'