Perfect Number Finder in a Range

Hard ⏱ 18 min 34% acceptance ★★★★☆ 4.4

Write a function perfect_numbers_in_range(start, end) that returns a list of all perfect numbers between start and end inclusive. A perfect number equals the sum of its proper divisors (divisors excluding itself), for example 6 = 1 + 2 + 3. Use nested loops: an outer loop over candidates and an inner loop to sum divisors.

Examples

Example 1

Input

perfect_numbers_in_range(1, 30)

Output

[6, 28]

Explanation

6 and 28 are the only perfect numbers in that range.

Example 2

Input

perfect_numbers_in_range(1, 5)

Output

[]

Explanation

No perfect numbers that small.

Constraints

1 <= start <= end.

Topics

Loopsnested loops

Companies

DeloitteAccenture

Hints

Hint 1

For each candidate number, sum all divisors from 1 up to candidate - 1 that evenly divide it.

Hint 2

A candidate is perfect if that sum equals the candidate itself (and the candidate is greater than 0).

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