P. Anantha Reddy, C. Sunitha and V. Siva Rama Prasad

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 26, 2020, Number 3, Pages 68—73

DOI: 10.7546/nntdm.2020.26.3.68-73

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## Details

### Authors and affiliations

P. Anantha Reddy

*Q.Q. Govt. Polytechnic
Chandulalbaradari, Hyderabad, Telangana-500064, India
*

C. Sunitha

*Department of Mathematics and Statistics, RBVRR Womens College*

Narayanaguda, Hyderabad, Telangana-500027, India

Narayanaguda, Hyderabad, Telangana-500027, India

V. Siva Rama Prasad

*Professor(Retired), Department of Mathematics, Osmania University*

Hyderabad, Telangana-500007, India

Hyderabad, Telangana-500007, India

### Abstract

For a positive integer *n*, let *σ*(*n*) and *ω*(*n*) respectively denote the sum of the positive divisors of *n* and the number of distinct prime factors of *n*. A positive integer *n* is called a quasimultiperfect (QM) number if *σ*(*n*) = *kn* + 1 for some integer *k* ≥ 2. In this paper we give some necessary conditions to be satisfied by the prime factors of QM number *n* with *ω*(*n*) = 3 and *ω*(*n*) = 4. Also we show that no QM *n* with *ω*(*n*) = 4 can be a fourth power of an integer.

### Keywords

- Quasimultiperfect number
- Quasitriperfect number

### 2010 Mathematics Subject Classification

- 11A25

### References

- Abbott, H. L., Aull, C. E., Brown, E., & Suryanarayana, D. (1973). Quasiperfect numbers, Acta Arithmetica, XXII, 439-447; Correction to the paper, Acta Arithmetica, XXIV (1976), 427–428.
- Cattaneo, P. (1951). Sui numeri quasiperfetti, Boll. Un. Mat. Ital., 6 (3), 59–62.
- Li, Meng, & Min, Tang. (2014). On the congruence
*σ*(*n*) ≡ 1 (mod n)-II, J. Math. Res. Appl., 34 (2), 155–160. - Min, Tang & Li, Meng. (2012). On the congruence
*σ*(*n*) ≡ 1 (mod n), J. Math. Res. Appl., 32 (6) 673–676. - Prasad, V. S. R., & Sunitha, C. (2017). On quasiperfect numbers, Notes on Number Theory and Discrete Mathematics, 23 (3), 73–78.
- Prasad, V. S. R., & Sunitha, C. (2019). On the prime factors of a quasiperfect number, Notes on Number Theory and Discrete Mathematics, 25 (2), 16–21.
- Sandor J., & Crstici, B. (2004). Handbook of Number Theory II, Kluwer Academic Publishers, Dordrecht/ Boston/ London.

## Related papers

- Prasad, V. S. R., & Sunitha, C. (2017). On quasiperfect numbers, Notes on Number Theory and Discrete Mathematics, 23 (3), 73–78.
- Prasad, V. S. R., & Sunitha, C. (2019). On the prime factors of a quasiperfect number, Notes on Number Theory and Discrete Mathematics, 25 (2), 16–21.

## Cite this paper

Reddy, P. A., Sunitha, C. & Prasad, V. S. R. (2020). On quasimultiperfect numbers. Notes on Number Theory and Discrete Mathematics, 26 (3), 68-73, doi: 10.7546/nntdm.2020.26.3.68-73.