On the Difference S(Z(n)) - Z(S(n)

In this paper, we prove that there exist infmitely many positive integers n satisfying S(Z(n))> Z(S(n)) or S(Z(n)) < Z(S(n))

THE CONRGENCE VALUE AND THE SIMPLE CONTINUED FRACTIONS OF SOME SMARANDACHE SEQUENCES

In this paper we consider the convergence value and the simple continued fraction of some Smarandache sequeces

THE LIMIT OF THE SMARANDACHE DIVISOR SEQUENCES

In this paper we prove that the limit T(n) of the Smarandache divisor sequence exists if and only if n is odd

The function equation S(n) = Z(n) 1

For any positive integer n, let S(n) and Z(n) denote the Smarandache function and the pseudo Smarandache function respectively. In this paper we prove that the equation S(n) = Z(n) has infinitely many positive integer solutions n

THE SMARANDACHE FRIENDLY NATURAL NUMBER PAIRS

In this paper we completely determinate all the Smarandache friendly natural number pairs

THE SQUARES IN THE SMARANDACHE FACTORIAL PRODUCT SEQUENCE OF THE SECOND KIND

In this paper one proves that the Smarandache factorial product sequence contains only one square 1

PERFECT POWERS IN THE SMARANDACHE PERMUTATION SEQUENCE

In this paper we prove that the Smarandache pennutation sequience does not contain perfect powers

ON THE BALU NUMBERS

In this paper we prove that there are only finitely many Balu numbers