A combinatorics Problem

  1. I am trying to find a way to calculate the number of positive integers less than n such that these numbers are not divisible by the prime numbers 2,3,5,7,11,13.

    If the problem were instead for prime numbers 2,3,5, then the solution is fairly simple. I used principle of inclusion and exclusion to solve the problem.

    for example if n=50

    [49/2] + [49/3] + [49/5] - [49/6] - [49/10] - [49/15] + [49/30] = 35

    49-35 = 14 integers under 50 that are not divisible by 2,3, or 5.

    At first i thought this method might be applicable if the question included primes: 2,3,5,7,11,13. But doing principle inclusion exclusion would take a Lot of calculator bashing. is there a smarter way to solve this problem for n= 60000
  2. jcsd
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