Mladen Vassilev-Missana

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 19, 2013, Number 3, Pages 24—27

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## Details

### Authors and affiliations

Mladen Vassilev-Missana

*5 V. Hugo Str., 1124 Sofia, Bulgaria*

### Abstract

In the paper the new formulae for the prime counting function *π*:

(where *σ* is the sum-of-divisor function and *ψ* is the Dedekind’s function) are proposed and proved. Also a general theorem (Theorem 1) is obtained that gives infinitely many explicit formulae for the prime counting function *π* (depending on arbitrary arithmetic function with strictly positive values, satisfying certain condition).

### Keywords

- Prime number
- Composite number
- Arithmetic function

### AMS Classification

- 11A25
- 11A41

### References

- Atanassov, K. T. Remark on Jacobsthal numbers, Part 2, Notes on Number Theory and Discrete Mathematics, Vol. 17, 2011, No. 2, 37–39.
- Atanassov, K. T. Short remarks on Jacobsthal numbers, Notes on Number Theory and Discrete Mathematics, Vol. 18, 2012, No. 2, 63–64.
- Rabago, J. F. T. Circulant Determinant Sequence with Binomial Coefficients, Scientia Magna (on review).
- Shang, Y. On the modifications of the Pell–Jacobsthal numbers, Scientia Magna, Vol. 8, 2012, No. 3, 68–70.

## Related papers

## Cite this paper

APAVassilev-Missana, M. (2013). New explicit representations for the prime counting function. Notes on Number Theory and Discrete Mathematics, 19(3), 24-27.

ChicagoVassilev-Missana, Mladen. “New Explicit Representations for the Prime Counting Function.” Notes on Number Theory and Discrete Mathematics 19, no. 3 (2013): 24-27.

MLAVassilev-Missana, Mladen. “New Explicit Representations for the Prime Counting Function.” Notes on Number Theory and Discrete Mathematics 19.3 (2013): 24-27. Print.