Count the number of positive integers less than 100 that do not contain any perfect square factors greater than 1.
Possible perfect squares are the squares of integers 2-9. In fact, only squares of primes need be considered, since for example, 6^2=36 actually contains factors 2^2 and 3^2. Tabulate the number (in [ ])of integers containing factors of 2^2=4: 4,8,12,16,...96 [24] 3^2=9: 9,18,....99 [11] 5^2=25: 25,50,75 [3] 7^2=49: 49,98 [2]
So the total number of integers from 1 to 99 N=24+11+3+2=40 => Number of positive square-free integers below 100 = 99-40 = 59
