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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 (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 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: A334958 A205957 A092144 * A305753 A181813 A059187 Adjacent sequences:  A224494 A224495 A224496 * A224498 A224499 A224500 KEYWORD nonn AUTHOR Peter Luschny, Apr 08 2013 STATUS approved

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Last modified September 19 12:49 EDT 2020. Contains 337178 sequences. (Running on oeis4.)