Smarandache Ceil Function

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.

where  is the number of solutions to .

The functions  for , 3, ..., 6 for values such that  are tabulated by Begay (1997). The following table gives  for small  and , 2, ....

	OEIS
1	A000027	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ...
2	A019554	1, 2, 3, 2, 5, 6, 7, 4, 3, 10, 11, 6, 13, 14, 15, 4, 17, 6, ...
3	A019555	1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 4, 17, 6, ...
4	A053166	1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, ...

REFERENCES:

Begay, A. "Smarandache Ceil Functions." Bull. Pure Appl. Sci. 16E, 227-229, 1997. https://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. https://mathworld.wolfram.com/news/2002-04-09/primeprimes/.