ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS

ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS

Autores

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

DOI:

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

Resumo

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

Como Citar

Alegri, M., Bulnes, J., Kim, T., & Bonilla, J. L. (2024). ARITHMETIC FUNCTIONS VERIFYING A RECURRENCE RELATION, COMPOSITIONS AND BELL POLYNOMIALS. Revista Sergipana De Matemática E Educação Matemática, 9(3), 25–34. https://doi.org/10.34179/revisem.v9i3.21793
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