Abundant Number Check

Determine if a positive integer is abundant by comparing its proper divisors to the number itself.

math divisors number-theory

A positive integer n is called an *abundant number* if the sum of its proper divisors (all positive divisors excluding n itself) is greater than n. For example, 12 has proper divisors 1, 2, 3, 4, 6 which sum to 16 > 12, so 12 is abundant. Write a function `is_abundant(n)` that returns `True` if n is abundant and `False` otherwise.

Constraints

1 <= n <= 10^5. The function must run in O(sqrt(n)) time.

Example

>>> is_abundant(12)
True
>>> is_abundant(18)
True
>>> is_abundant(15)
False

10 points ~15 min

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Hints

Find divisors up to the square root of n.

Remember to exclude n itself when summing proper divisors.

Make sure to handle n=1 correctly (sum of proper divisors is 0).

Test Results

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