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A224497
a(n) = sqrt(floor(n/2)! * Product_{k=1..n} Product_{i=1..k-1} gcd(k,i)).
2
1, 1, 1, 1, 2, 2, 12, 12, 96, 288, 5760, 5760, 829440, 829440, 46448640, 2090188800, 267544166400, 267544166400, 346737239654400, 346737239654400, 1109559166894080000, 209706682542981120000, 73816752255129354240000, 73816752255129354240000
OFFSET
0,5
COMMENTS
The order of the primes in the prime factorization of a(n) is given by
ord_{p}(a(n)) = (1/4)*Sum_{i>=1} floor(n/p^i)*(floor(n/p^i)-1) + (1/2)*Sum_{i>=1} floor(floor(n/2)/p^i).
For n > 1: a(n) = a(n-1) if and only if n is prime.
FORMULA
a(n) = sqrt(floor(n/2)! * A224479(n)).
A092287(n) = A056040(n) * a(n)^4.
MAPLE
A224497 := n -> sqrt(iquo(n, 2)!*mul(mul(igcd(k, i), i=1..k-1), k=1..n)):
seq(A224497(i), i = 0..23);
PROG
(Sage)
def A224497(n):
R = 1;
for p in primes(n):
s = 0; t = 0
r = n; u = n//2
while r > 0 :
r = r//p; u = u//p
t += u; s += r*(r-1)
R *= p^((t+s/2)/2)
return R
[A224497(i) for i in (0..23)]
CROSSREFS
Cf. A224479.
Sequence in context: A205957 A341432 A092144 * A305753 A181813 A059187
KEYWORD
nonn
AUTHOR
Peter Luschny, Apr 08 2013
STATUS
approved