In the work we apply the Z-transform to the recurrence of Cauchy convolution type, satisfied by several arithmetic functions, to obtain its solution in terms of the complete Bell polynomials. One of the most important arithmetic function used here is sigma1(n), the function that sum all positive divisors of n. Our main result can be applied to find a closed formula for the number of k-colored partitions, sum of triangular numbers and more.

In the work we apply the Z-transform to the recurrence of Cauchy convolution type, satisfied by several arithmetic functions, to obtain its solution in terms of the complete Bell polynomials. One of the most important arithmetic function used here is sigma1(n), the function that sum all positive divisors of n. Our main result can be applied to find a closed formula for the number of k-colored partitions, sum of triangular numbers and more.

Autores/as

  • Mateus Alegri Universidade Federal de Sergipe
  • Juan Bulnes
  • Taekyun Kim
  • José Luís Bonilla

DOI:

https://doi.org/10.34179/revisem.v9i3.21793

Resumen

In the work we apply the Z-transform to the recurrence of Cauchy convolution type, satisfied by several arithmetic functions, to obtain its solution in terms of the complete Bell polynomials. One of the most important arithmetic function used here is sigma1(n), the function that sum all positive divisors of n. Our main result can be applied to find a closed formula for the number of k-colored partitions, sum of triangular numbers and more.

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Publicado

2024-10-14

Cómo citar

Alegri, M., Bulnes, J., Kim, T., & Bonilla, J. L. (2024). In the work we apply the Z-transform to the recurrence of Cauchy convolution type, satisfied by several arithmetic functions, to obtain its solution in terms of the complete Bell polynomials. One of the most important arithmetic function used here is sigma1(n), the function that sum all positive divisors of n. Our main result can be applied to find a closed formula for the number of k-colored partitions, sum of triangular numbers and more. Revista Sergipana De Matemática E Educação Matemática, 9(3), 25–34. https://doi.org/10.34179/revisem.v9i3.21793

Número

Vol. 9 Núm. 3 (2024): Revista Sergipana de Matemática e Educação Matemática

Sección

Matemática

Licencia

Derechos de autor 2024 Mateus Alegri

Creative Commons License

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