Smarandache Ceil Function
A Smarandache-like function which is defined where 
is defined as the smallest integerfor 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 
aretabulated 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, andA000027/M0472in ``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.
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