**A. G. Shannon**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 2, Pages 113-126

DOI: 10.7546/nntdm.2019.25.2.113-126

**Full paper (PDF, 153 Kb)**

## Details

### Authors and affiliations

A. G. Shannon

*Fellow, Warrane College, The University of New South Wales
Kensington NSW 2033, Australia
*

### Abstract

This paper extends some of the arithmetic functions which Mollie Horadam developed for sequences of generalized integers and apply them to some particular integer sequences, particularly the Fibonacci and Fermatian numbers.

### Keywords

- Fermatian numbers
- Lucas numbers
*q*-Bernoulli numbers- Divisibility sequences
- Ramanujan’s sum
- Möbius function
- Totient functions
- Co-prime
- Fibonacci numbers

### 2010 Mathematics Subject Classification

- 11B75
- 11Z05
- 11B65

### References

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## Related papers

- Akkuş, H., Deveci, Ö, Özkan, E., & Shannon, A. G. (2024). Discatenated and lacunary recurrences.
*Notes on Number Theory and Discrete Mathematics*, 30(1), 8-19.

## Cite this paper

Shannon, A. G. (2019). Applications of Mollie Horadam’s generalized

integers to Fermatian and Fibonacci numberss. *Notes on Number Theory and Discrete Mathematics*, 25(2), 113-126, DOI: 10.7546/nntdm.2019.25.2.113-126.