Ashbacher, An introduction to the Smarandache function
, Erhus Univ.
The pseudo Smarandache function
, Z(n), introduced by Kashihara , is as follows:
For any positive integer n, the Smarandache function
S(n) can be defined as follows: S(n) is the smallest number, such that S(n)
This paper as a note of Gou Su's work, we consider the hybrid mean value properties of the Smarandache kn-digital sequence and Smarandache function
S(n), which is defined as the smallest positive integer m such that n|m
5] Du Fengying, On a conjecture of the Smarandache function
S(n), 23(2007), No.
Since then, the pseudo Smarandache function
has seen several generalizations in different directions.
1] Wenpeng Zhang and Ling Li, Two problems related to the Smarandache function
, Scientia Magna, Vol.
9] Xu Zhefeng, The value distribution property of the Smarandache function
, Acta Mathematica Sinica, Chinese Series, Vol.
one obtains the Smarandache function
S(n), and its dual S*(n), given by
Sandor, On certain generalizations of the Smarandache function
, Smarandache Notions Journal, 11(2000), No.
Mark, NLPatrick, Bounding the Smarandache function
, Smarandache Notions Journal, 13(2002), 37-42.
4] Xu Zhefeng, On the value distribution of the Smarandache function
, Acta Mathematics Sinks (in Chinese), 49(2006), No.