Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 57: Issue 2
Some properties of harmonic numbers
Authors: Bing-Ling Wu1 and Xiao-Hui Yan2
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  • 1 School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, P. R. China
  • | 2 School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, P. R. China and School of Mathematics and Statistics, Anhui Normal University, Wuhu 241003, P. R. China
Pages:
207–216
Online Publication Date:
Jun 2020
Publication Date:
01 Jun 2020
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2020.57.2.1458
Keywords:
Harmonic numbers; logarithmic density; prime; denominator
Restricted access

Abstract

Let Hn be the n-th harmonic number and let vn be its denominator. It is known that vn is even for every integer n>=2. In this paper, we study the properties of Hn and prove that for any integer n, vn = en(1+o(1)). In addition, we obtain some results of the logarithmic density of harmonic numbers.

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    Duncan, R. L., Note on the initial digit problem, Fibonacci Quart ., 7(5 ) (1969), 474–475.

  • [3]

    Eswarathasan, A. and Levine, E., p-integral harmonic sums, Discrete Math ., 91(3 ) (1991), 249–257.B.-L. WU and X.-H. YAN: Some Properties of Harmonic Numbers.

    • Crossref
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  • [4]

    LEONETTI, P. and Sanna, C., On the p-adic valuation of Stirling numbers of the first kind, Acta Math. Hungar., 151 (2017), 217–231.

  • [5]

    SANNA, C., On the p-adic valuation of harmonic numbers, J. Number Theory, 166 (2016), 41–46.

  • [6]

    SHIU, P., The denominators of harmonic numbers, arXiv:1607.02863v1.

  • [7]

    Wu, B. L. and Chen, Y. G., On certain properties of harmonic numbers, J. Number Theory, 175 (2017), 66–86.

  • [8]

    Wu, B. L. and Chen, Y. G., On the denominators of harmonic numbers, C. R. Acad. Sci. Paris, Ser I 356 (2018), 129–132.

  • [9]

    Wu, B. L. and Chen, Y. G., On the denominators of harmonic numbers, II, J. Number Theory, 200 (2019), 397–406.

Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
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Indexing and Abstracting Services:

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2021  
Web of Science  
Total Cites
WoS		 589
Journal Impact Factor 0,739
Rank by Impact Factor Mathematics 229/332
Impact Factor
without
Journal Self Cites		 0,710
5 Year
Impact Factor		 0,654
Journal Citation Indicator 0,57
Rank by Journal Citation Indicator Mathematics 287/474
Scimago  
Scimago
H-index		 26
Scimago
Journal Rank		 0,265
Scimago Quartile Score Mathematics (miscellaneous) (Q3)
Scopus  
Scopus
Cite Score		 1,3
Scopus
CIte Score Rank		 General Mathematics 193/391 (Q2)
Scopus
SNIP		 0,746

2020  
Total Cites 536
WoS
Journal
Impact Factor		 0,855
Rank by Mathematics 189/330 (Q3)
Impact Factor  
Impact Factor 0,826
without
Journal Self Cites
5 Year 1,703
Impact Factor
Journal  0,68
Citation Indicator  
Rank by Journal  Mathematics 230/470 (Q2)
Citation Indicator   
Citable 32
Items
Total 32
Articles
Total 0
Reviews
Scimago 24
H-index
Scimago 0,307
Journal Rank
Scimago Mathematics (miscellaneous) Q3
Quartile Score  
Scopus 139/130=1,1
Scite Score  
Scopus General Mathematics 204/378 (Q3)
Scite Score Rank  
Scopus 1,069
SNIP  
Days from  85
submission  
to acceptance  
Days from  123
acceptance  
to publication  
Acceptance 16%
Rate

2019  
Total Cites
WoS		 463
Impact Factor 0,468
Impact Factor
without
Journal Self Cites		 0,468
5 Year
Impact Factor		 0,413
Immediacy
Index		 0,135
Citable
Items		 37
Total
Articles		 37
Total
Reviews		 0
Cited
Half-Life		 21,4
Citing
Half-Life		 15,5
Eigenfactor
Score		 0,00039
Article Influence
Score		 0,196
% Articles
in
Citable Items		 100,00
Normalized
Eigenfactor		 0,04841
Average
IF
Percentile		 13,117
Scimago
H-index		 23
Scimago
Journal Rank		 0,234
Scopus
Scite Score		 76/104=0,7
Scopus
Scite Score Rank		 General Mathematics 247/368 (Q3)
Scopus
SNIP		 0,671
Acceptance
Rate		 14%

 

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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