Abstract

We study the distribution of the sequence of integers $2^{\omega (n)}$ under the assumption of the strong Riemann hypothesis, where $\omega (n)$ denotes the number of distinct prime divisors of $n$. We provide an asymptotic formula for the sum ${\sum <!--FUNCTION\; APPLICATION-->}_{n\le x}{2}^{\omega (n)}$ under this assumption. We also study the sum ${\sum <!--FUNCTION\; APPLICATION-->}_{n\le x}{2}^{\omega (n)}$ unconditionally.

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