A recurrence formula for prime numbers using the Smarandache or Totient functions

A functional recurrence to obtain the prime numbers using the Smarandache prime function

On Totient Abundant Numbers

In this note, we find an asymptotic formula for the counting function of the set of totient abundant numbers.

On a problem concerning the Smarandache Unary sequence

In this paper a problem posed in [1J and concerning the number of primes in the Smarandache Unary sequence is analysed. Introduction In [1] the Smarandache Unary sequence is defined as the sequence obtained concatenating Pn digits of 1, where Pn is the n-th prime number: 11,111,11111,1111111,11111111111,1111111111111,11111111111111111, ......... . In the same paper the following open question i...

On some Smarandache conjectures and unsolved problems

In this paper some Smarandache conjectures and open questions will be analysed. The first three conjectures are related to prime numbers and formulated by F. Smarandache in [1].

On the mean value of the Pseudo-Smarandache function

For any positive integer n, the Pseudo-Smarandache function Z(n) is defined as the smallest positive integer k such that n | k(k + 1) 2 . That is, Z(n) = min { k : n| + 1) 2 } . The main purpose of this paper is using the elementary methods to study the mean value properties of p(n) Z(n) , and give a sharper asymptotic formula for it, where p(n) denotes the smallest prime divisor of n.