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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).
See also Pseudosmarandache Function, Smarandache Function, Smarandache-Kurepa Function, Smarandache Near-to-Primorial Function, Smarandache Sequences, Smarandache-Wagstaff Function
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.