On the distribution of the strongly multiplicative function $2^{ω(n)}$ on the set of natural numbers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916597859352576 |
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| author | Venkatasubbareddy, K. Sankaranarayanan, A. |
| author_facet | Venkatasubbareddy, K. Sankaranarayanan, A. |
| contents | In this paper, we study the distribution of the sequence of integers $2^{ω(n)}$ 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 $\displaystyle\sum_{n\leq x}2^{ω(n)}$ under this assumption. We study the sum $\displaystyle\sum_{n\leq x}2^{ω(n)}$ unconditionally too. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_02598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the distribution of the strongly multiplicative function $2^{ω(n)}$ on the set of natural numbers Venkatasubbareddy, K. Sankaranarayanan, A. Number Theory In this paper, we study the distribution of the sequence of integers $2^{ω(n)}$ 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 $\displaystyle\sum_{n\leq x}2^{ω(n)}$ under this assumption. We study the sum $\displaystyle\sum_{n\leq x}2^{ω(n)}$ unconditionally too. |
| title | On the distribution of the strongly multiplicative function $2^{ω(n)}$ on the set of natural numbers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2502.02598 |