compositorial

Iago Camboa pointed out that n!/n# (n-factorial divided by n-primorial) is the product of all the composite numbers less than or equal to n and suggested the name compositiorial.

The numbers n!/n# ± 1 (when prime) might be given the name compositorial prime (like factorial prime and primorial prime).  For example, Daniel Heuer noted the primes of these forms with n < 10000 are

form n!/n#+1:

(1,2,3), (4,5), 8, 14, 20, 26, 34, 56, 104, 153, 182, 194, 217, 230, (280, 281), (462,463), 529, 1445, 2515

form n!/n#-1

(4,5), (6,7), 8, (16,17), 21, 34, 39, 45, 50, (72,73), 76, 133, 164, 202, 216, 221, (280,281), 496, 605, 2532, 2967, 3337

(Values of n grouped in parenthesis yield the same prime.)

Notice that 280!/280# ± 1 (= 281!/281# ± 1) are twin primes!