Quote:
Originally Posted by ThiloHarich
Sorry.
The sum of all divisors  not the prime divisors I thought of  can be higher then the number itself. So I misinterpreted your model.
So yes abundant numbers https://en.wikipedia.org/wiki/Abundant_number are good candidates.
But for example 105 and 15 are no such numbers but are good 'k'.

Sum means here the amount, quantity.