Abstract
For lack of a better word, a number is called special if it has mutually distinct exponents in its canonical prime factorizaton for all exponents. Let V(x) be the number of special numbers ≤x. We will prove that there is a constant c>1 such that \(\displaystyle {V(x) \sim \frac {cx}{\log x}}\). We will make some remarks on determining the error term at the end. Using the explicit abc conjecture, we will study the existence of 23 consecutive special integers.
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