is the smallest prime such that , , or is divisible by , where is the primorial of . Ashbacher (1996) shows that only exists
1. If there are no square or higher powers in the factorization of , or
2. If there exists a prime such that , where is the smallest power contained in the factorization of .
Therefore, does not exist for the squareful
numbers , 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, ... (OEIS A013929).
The first few values of , where defined, are 2, 2, 2, 3, 3, 3, 5, 7, ... (OEIS
A046026).
Ashbacher, C. "A Note on the Smarandache Near-To-Primordial 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 
, where 
is the primorial of 
. Ashbacher (1996) shows that 
only exists
, or
such that 
, where 
is the smallest power contained in the factorization of 
.
does not exist for the squareful
numbers 
, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, ... (OEIS A013929).
The first few values of 
, where defined, are 2, 2, 2, 3, 3, 3, 5, 7, ... (OEIS
A046026).
