Some representations concerning the product of divisors of n

Mladen V. Vassilev-Missana
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 10, 2004, Number 2, Pages 54–56
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Mladen Vassilev-Missana
V. Hugo Str. 5, Sofia-1124, Bulgaria

Abstract

Let us denote by \tau(n) the number of all divisors of n. It is well-known (see, e.g.,  [1]) that

(1)   \begin{align*}P_d(n)=\sqrt{n^{\tau(n)}} \end{align*}

and of course, we have

(2)   \begin{align*}p_d(n)=\frac{P_d(n)}{n} \end{align*}

But (1) is not a good formula for P_d(n), because it depends on function \tau  and to express \tau(n)  we need the prime number factorization of n.

Below, we give other representations of P_d(n) and p_d(n), which do not use the prime number factorization of n.

References

  1. Nagell T., Introduction to Number Theory. John Wiley & Sons, Inc., New York, 1950.

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Cite this paper

Vassilev-Missana, M. (2004). Some representations concerning the product of divisors of n. Notes on Number Theory and Discrete Mathematics, 10(2), 54-56.

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