The Smarandache near-to-primorial function is the smallest prime
such that , , or is divisible by the positive
integer, where is the primorial of . The value exists iff one of the following
conditions holds (Ashbacher 1996):
For example, is undefined at , 8, 9, 12, 16, 18, 20, 24, 25, 27, and 28, the initial squareful numbers (OEIS A013929),
since none satisfies the second condition. For the squarefree
arguments , 2, 3, 5, 6, 7, 10, 11, ..., the first few values of
are 2, 2, 2, 3, 3, 3, 5, 7, ... (OEIS A046026).
Ashbacher, C. "A Note on the Smarandache Near-To-Primorial Function." Smarandache Notions J.7, 46-49, 1996.Mudge,
M. R. "The Smarandache Near-To-Primorial Function." Abstracts of
Papers Presented to the Amer. Math. Soc.17, 585, 1996.Sloane,
N. J. A. Sequences A013929 and A046026 in "The On-Line Encyclopedia of Integer
Sequences."
is the smallest prime 
such that 
, 
, or 
is divisible by the positive
integer 
, where 
is the primorial of 
. The value 
exists iff one of the following
conditions holds (Ashbacher 1996):
is squarefree.
is not squarefree and there
exists a prime 
such that 
, where 
is the least prime factor
of 
.
is undefined at 
, 8, 9, 12, 16, 18, 20, 24, 25, 27, and 28, the initial squareful numbers (OEIS A013929),
since none satisfies the second condition. For the squarefree
arguments 
, 2, 3, 5, 6, 7, 10, 11, ..., the first few values of 
are 2, 2, 2, 3, 3, 3, 5, 7, ... (OEIS A046026).
