A Smarandache-like function which is defined where is defined as the smallest integer for which . The Smarandache function can therefore be obtained by replacing any factors which are th powers in by their roots. The functions for , 3, ..., 6 for values such that are tabulated by Begay (1997).

, so the first few values of are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, ... (Sloane's A000027). The first few values of are 1, 2, 3, 2, 5, 6, 7, 4, 3, 10, 11, 6, 13, 14, 15, 4, 17, 6, 19, 10, ... (Sloane's A019554) The first few values of are 1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 4, 17, 6, 19, 10, ... (Sloane's A019555) The first few values of are 1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, 19, 10, ... (Sloane's A007947).

**References**

Begay, A. ``Smarandache Ceil Functions.'' *Bull. Pure Appl. Sci.* **16E**, 227-229, 1997.

``Functions in Number Theory.'' http://www.gallup.unm.edu/~smarandache/FUNCT1.TXT.

Sloane, N. J. A. Sequences A007947, A019554, A019555, and A000027/M0472 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.

Smarandache, F. *Collected Papers, Vol. 2.* Kishinev, Moldova: Kishinev University Press, 1997.

Smarandache, F. *Only Problems, Not Solutions!, 4th ed.* Phoenix, AZ: Xiquan, 1993.

© 1996-9

1999-05-26