Some representations concerning the product of divisors of n

Mladen V. Vassilev-Missana and Krassimir T. Atanassov
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 τ(n) the number of all divisors of n. It is well-known (see, e.g., ) that

P_d(n) = \sqrt{n^{\tau(n)}} (1)

and of course, we have

p_d(n) = \frac{P_d(n)}{n}. (2)

But (1) is not a good formula for Pd(n), because it depends on function τ and to express τ(n) we need the prime number factorization of n.
Below, we give other representations of Pd(n) and pd(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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