ON THE MERCA'S CONNECTION BETWEEN THE PARTITION FUNCTION AND EULER'S TOTIENT

ON THE MERCA'S CONNECTION BETWEEN THE PARTITION FUNCTION AND EULER'S TOTIENT

Auteurs

  • Mateus Alegri Universidade Federal de Sergipe
  • José Luís Bonilla
  • J. Prajapati

DOI :

https://doi.org/10.34179/revisem.v9i3.21794

Résumé

We employ the Z-transform to study a result of Merca involving the partition function $p(n)$ and Euler's totient. Besides, we obtain an identity valid for pentagonal numbers and an arbitrary prime number.

Keywords: Partition function, Dirichlet character, Euler totient function, Z-transform, Möbius function.

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Publiée

2024-10-14

Comment citer

Alegri, M., Bonilla, J. L., & Prajapati, J. (2024). ON THE MERCA’S CONNECTION BETWEEN THE PARTITION FUNCTION AND EULER’S TOTIENT. Revista Sergipana De Matemática E Educação Matemática, 9(3), 136–143. https://doi.org/10.34179/revisem.v9i3.21794

Numéro

Vol. 9 No 3 (2024): Revista Sergipana de Matemática e Educação Matemática

Rubrique

Matemática

Licence

(c) Tous droits réservés Mateus Alegri 2024

Creative Commons License

Ce travail est disponible sous licence Creative Commons Attribution - Pas d’Utilisation Commerciale 4.0 International.

Licença Creative Commons

  Permite remixagem, adaptação e nova criação a partir da obra para fins não comerciais, e que seja atribuído o crédito ao autor (CC BY-NC)