Untouchable Numbers

A positive number greater than 1 can be defined untouchable when it's not equal to the sum of the proper divisors (called also aliquot sum) of any other positive number, in a range starting from 2 and ending with the square of the given number (bounds included).

Given an integer number, implement a function that returns:

• True if the given number is untouchable.
• A list containing the numbers whose proper divisors sum is equal to the number, if the given number is not untouchable.
• A string "Invalid Input" if the given number is lower than 2.

Examples

is_untouchable(2) ➞ True
# Range: 2 to 4
# 2 = 1  |  3 = 1  |  4 = 1+2 = 3
# No sum is equal to the given number

is_untouchable(3) ➞ [4]
# Range: 2 to 9
# As in the example above, 4 = 1+2 = 3

is_untouchable(6) ➞ [6, 25]
# Range: 2 to 36
# 6 = 1+2+3 = 6  |  25 = 1+5 = 6

is_untouchable(1) ➞ "Invalid Input"
# The given number is lower than 2

Notes

• The proper divisors of a number are, merely, all its divisors less the number itself.
• More than a number can have a proper divisors sum equal to the given number, with given number included (see example #3).
• Trivia: As far as we know, numbers 2 and 5 are the only two primes present in the sequence, with 5 being the only odd number present; by the way, these two assertions are still unproofed.