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Smarandache Ceil Function


A Smarandache-like function which is defined where S_k(n) is defined as the smallest integer for which n|S_k(n)^k. The Smarandache S_k(n) function can therefore be obtained by replacing any factors which are kth powers in n by their k roots.

 S_k(n)=n/(M_k(n)),

where M_k(n) is the number of solutions to x^k=0 (mod n).

The functions S_k(n) for k=2, 3, ..., 6 for values such that S_k(n)!=n are tabulated by Begay (1997). The following table gives S_k(n) for small k and n=1, 2, ....

kOEISS_k(n)
1A0000271, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ...
2A0195541, 2, 3, 2, 5, 6, 7, 4, 3, 10, 11, 6, 13, 14, 15, 4, 17, 6, ...
3A0195551, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 4, 17, 6, ...
4A0531661, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, ...

See also

Pseudosmarandache Function, Smarandache Function, Smarandache-Kurepa Function, Smarandache Near-to-Primorial Function, Smarandache Sequences, Smarandache-Wagstaff Function

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References

Begay, A. "Smarandache Ceil Functions." Bull. Pure Appl. Sci. 16E, 227-229, 1997. http://www.gallup.unm.edu/~smarandache/smarceil.htm.Sloane, N. J. A. Sequences A000027/M0472, A019554, A019555, and A053166 in "The On-Line Encyclopedia of Integer Sequences."Smarandache, F. Collected Papers, Vol. 2. Kishinev, Moldova: Kishinev University Press, 1997.Smarandache, F. Only Problems, Not Solutions!, 4th ed. Phoenix, AZ: Xiquan, 1993.Weisstein, E. W. "Gigantic Primes with Prime Digits Found." MathWorld Headline News, Apr. 9, 2002. http://mathworld.wolfram.com/news/2002-04-09/primeprimes/.

Referenced on Wolfram|Alpha

Smarandache Ceil Function

Cite this as:

Weisstein, Eric W. "Smarandache Ceil Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SmarandacheCeilFunction.html

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