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

AI Thread Summary
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.
Swamp Thing
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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 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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