a1 Department of Mathematics, Nanjing Normal University, Nanjing, 210097, China, e-mail: firstname.lastname@example.org
Let p be a prime and m be a positive integer. For a positive integer n, let ep(n) be the nonnegative integer with pep(n) | n and pep(n)+1 n. As a corollary of our main result we derive an asymptotic formula for the counting function with regard to the condition ep(n!) ≡ (mod 3), where Z3. In 2001, Sander proved the result with modulus 2.
(Received October 10 2005)