How many numbers n<100 are not divisible by a square of any integer greater than 1?

trkalo84 2022-09-22 Answered
How many numbers n < 100 are not divisible by a square of any integer greater than 1?
Working through the above counting problem. I got 48 using the Inclusion-Exclusion Principle, do you agree?
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Answers (1)

niveaus7s
Answered 2022-09-23 Author has 8 answers
I don't see how you got to 48.

I assume we're working in the natural numbers so 99 numbers less than 100 all together. Any number divisible by a square number > 1 is divisible by a prime square.
1. 24 are divisible by 4.
2. 11 are divisible by 9 - two of which (36 and 72) are already counted above.
3. 3 are divisible by 25,
4. 2 are divisible by 49
Total of 24+(11−2)+3+2=38 are divisible by squares > 1, so 61 numbers < 100 are not divisible by a square number > 1.
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