How many of the numbers from the set \(\{1,\ 2,\ 3,\ldots,\ 50\} \) have a perfect square factor other than one?
These are the ones I can think of:
(8, 12, 16, 18, 20, 24, 27, 28, 32, 36, 40, 44, 45, 48, 50)=15
Rom has interpreted the question a bit differently from me. :)
All the multiples of 4
4,8,12,16,20,24,28,32,36,40,44,48
All the multiples of 9 that you do not already have
9,18,27, not36, 45
you already have all the multiples of 16
All the multiples of 25
25, 50
you already have all the multiples of 36
All the multiples of 49
so that is
4, 8, 9, 12,16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50 So I count 19 of them.