On a Sum Involving the Sum-of-Divisors Function
Let σn be the sum of all divisors of n and let t be the integral part of t. In this paper, we shall prove that ∑n≤xσx/n=π2/6x log x+Oxlog x2/3log2 x4/3 for x⟶∞, and that the error term of this asymptotic formula is Ωx.
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5574465 |
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| _version_ | 1832554024379875328 |
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| author | Feng Zhao Jie Wu |
| author_facet | Feng Zhao Jie Wu |
| author_sort | Feng Zhao |
| collection | DOAJ |
| description | Let σn be the sum of all divisors of n and let t be the integral part of t. In this paper, we shall prove that ∑n≤xσx/n=π2/6x log x+Oxlog x2/3log2 x4/3 for x⟶∞, and that the error term of this asymptotic formula is Ωx. |
| format | Article |
| id | doaj-art-891cb86df89849ea8507925a1640cf10 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-891cb86df89849ea8507925a1640cf102025-02-03T05:52:39ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55744655574465On a Sum Involving the Sum-of-Divisors FunctionFeng Zhao0Jie Wu1Department of Mathematics and Statistics, North China University of Water Resources and Electric Power, Jinshui E Road, Zhengzhou 450046, Henan, ChinaCNRS LAMA 8050, Laboratoire D’Analyse et de Mathématiques Appliquées, Université Paris-Est Créteil, Créteil Cedex 94010, FranceLet σn be the sum of all divisors of n and let t be the integral part of t. In this paper, we shall prove that ∑n≤xσx/n=π2/6x log x+Oxlog x2/3log2 x4/3 for x⟶∞, and that the error term of this asymptotic formula is Ωx.http://dx.doi.org/10.1155/2021/5574465 |
| spellingShingle | Feng Zhao Jie Wu On a Sum Involving the Sum-of-Divisors Function Journal of Mathematics |
| title | On a Sum Involving the Sum-of-Divisors Function |
| title_full | On a Sum Involving the Sum-of-Divisors Function |
| title_fullStr | On a Sum Involving the Sum-of-Divisors Function |
| title_full_unstemmed | On a Sum Involving the Sum-of-Divisors Function |
| title_short | On a Sum Involving the Sum-of-Divisors Function |
| title_sort | on a sum involving the sum of divisors function |
| url | http://dx.doi.org/10.1155/2021/5574465 |
| work_keys_str_mv | AT fengzhao onasuminvolvingthesumofdivisorsfunction AT jiewu onasuminvolvingthesumofdivisorsfunction |