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On the distribution of the strongly multiplicative function $2^{\omega(n)}$ on the set of natural numbers

Kampamolla Venkatasubbareddy and Ayyadurai Sankaranarayanan
Vol. 15 (2026), No. 2, 147–157
DOI: 10.2140/cnt.2026.15.147
Abstract

We study the distribution of the sequence of integers 2ω(n) under the assumption of the strong Riemann hypothesis, where ω(n) denotes the number of distinct prime divisors of n. We provide an asymptotic formula for the sum ∑ ⁡ n≤x2ω(n) under this assumption. We also study the sum ∑ ⁡ n≤x2ω(n) unconditionally.

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Keywords
Dirichlet series, Riemann zeta function, Riemann hypothesis, Perron formula
Mathematical Subject Classification
Primary: 11M06, 11M26
Milestones
Received: 10 December 2025
Revised: 17 April 2026
Accepted: 2 May 2026
Published: 10 May 2026
Authors
Kampamolla Venkatasubbareddy
School of Mathematics and Statistics
University of Hyderabad
Hyderabad
India		 Department of Mathematical Sciences
IISER Berhampur
Berhampur
India
Ayyadurai Sankaranarayanan
School of Mathematics and Statistics
University of Hyderabad
Hyderabad
India
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