login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..23.

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: A025527 A205957 A092144 * A305753 A181813 A059187

Adjacent sequences:  A224494 A224495 A224496 * A224498 A224499 A224500

KEYWORD

nonn

AUTHOR

Peter Luschny, Apr 08 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 20 20:46 EST 2019. Contains 329347 sequences. (Running on oeis4.)