This may seem like a weird question, but how to find the numbers with non-exponential prime factors i.e. numbers which specifically have primes that occur only once in its prime-factorization. For eg: $15=3×5$, $70=2×5×7$. So, 15 and 70 are such numbers which have prime-factors that occur only once in its prime-factorization.
$28=7×4$. In its prime-factorization = $7×2×2$ So, 28 is NOT a number which has prime-factors that occur only once.
So, is there any way to find such numbers??
Thank you.
There is an algorithm for "detecting square free numbers". See for example the article by Andrew R. Booker, Ghaith A. Hiary, Jon P. Keating:
"We present an algorithm, based on the explicit formula for $L$-functions and conditional on the generalized Riemann hypothesis, for proving that a given integer is squarefree with little or no knowledge of its factorization. We analyze the algorithm both theoretically and practically and use it to prove that several RSA challenge numbers are not squarefull."