How many numbers from 2 to 50 are not prime and are such that neither the number nor double the number is divisible by a perfect square greater than 1?

Answer 1

Interesting question! OK, first of all the perfect squares between 2 to 100 are:

4,9,16,25,36,49,64,81 & 100.

The prime numbers between 2 and 50 are:

2,3,5,7,11,13,17,19,23,29,31,37,41,43 & 47.

This leaves all other numbers between 2 to 50 to consider.

However, all even numbers from 4 onward will either themselves or their doubles divide by 4, so we only need consider the odd numbers.

The numbers which therefore meet this criteria are:

15, 21, 33 & 39

Therefore the answer is 4.