OFFSET
0,3
COMMENTS
a(n) are the partial products of A219964(n).
a(n) divides n!, n!/a(n) = 1, 1, 1, 1, 2, 2, 4, 4, 8, 72, 144, 144, 192...
The swinging factorial (A056040) divides a(n), a(n)/n$ = 1, 1, 1, 1, 2,...
The primorial of n (A034386) divides a(n), a(n)/n# = 1, 1, 1, 1, 2, 2, 6,..
If p^k is the largest power of a prime dividing a(n) then k is 2^n for some n >= 0.
MAPLE
a := proc(n) local k; `if`(n < 2, 1,
mul(k, k = select(isprime, [$iquo(n, 2)+1..n]))*a(iquo(n, 2))^2) end:
seq(a(i), i=0..25);
PROG
(Sage)
def a(n) :
if n < 2 : return 1
return mul(k for k in prime_range(n//2+1, n+1))*a(n//2)^2
[a(n) for n in (0..25)]
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Mar 30 2013
STATUS
approved