OFFSET
1,6
COMMENTS
A non-unitary prime divisor for n! cannot exceed n/2.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = pi(n/2).
A prime divisor of x is non-unitary iff its exponent is at least 2 in the prime power factorization of x. In general, GCD(p, x/p) = 1 or p. Cases are counted when GCD(p, n/p) > 1.
a(n) = A056170(n!). - Amiram Eldar, Jul 24 2024
EXAMPLE
10! = 2^8 * 3^4 * 5^2 * 7. The non-unitary prime divisors are 2, 3, and 5 because their exponents exceed 1, so a(10) = 3. The only unitary prime divisor of 10! is 7.
MAPLE
with(numtheory); A056172:=n->pi(floor(n/2)); seq(A056172(k), k=1..100); # Wesley Ivan Hurt, Sep 30 2013
MATHEMATICA
Table[PrimePi[Floor[n/2]], {n, 100}] (* Wesley Ivan Hurt, Sep 30 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Jul 27 2000
EXTENSIONS
Example corrected by Jon E. Schoenfield, Sep 30 2013
STATUS
approved