Undergrad Union of Prime Numbers & Non-Powers of Integers: Usage & Contexts

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The discussion centers on the union of prime numbers and integers that are not powers of integers, questioning if there is a specific name for this set. It highlights that prime numbers are a subset of the larger group of non-perfect powers. Participants note that this union includes numbers like 2, 3, 5, 6, 10, and 12, while excluding perfect powers such as 2^n and 3^n. The conversation also touches on the contexts in which this set may appear, though it acknowledges the simplicity of the question. Ultimately, the union is recognized as a combination of primes and non-perfect powers, emphasizing its mathematical significance.
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Is there a name for the union of {prime numbers} and {integers that are not powers of integers}?

For example, we would include 2, 3, 5, 7, 11... And also 6, 10, 12...

But we exclude 2^n, 3^n, ... and 6^n , 10^n , etc.

What are some interesting contexts where this set crops up?
 
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A rather silly question, I now realize : The first set is a subset of the second one anyway. And they are just "not perfect powers".
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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