An Equivalent Form of the Prime Number Theorem - Reddy, G. Sudhaamsh Mohan; Rau, S. Srinivas; Uma, B. (Sarajevo Journal of Mathematics, 2020)
A simple proof is given that _nμ(n) d(n)n=0 using the Prime Number Theorem. It is shown that this is equivalent to the estimate _n≤ xμ(n)d(n)=°(x) and to the Prime Number Theorem.