|
|
A109914
|
|
Product of all composite numbers k such that n! < k < prime(r) where prime(r-1)< n!.
|
|
2
|
|
|
1, 1, 1, 491400, 3546112878000, 143424700959632400, 10691567972893973348743970911396896000, 210948344078434820704169472200928966427054605885088717074131707385374604732966434908020301638860800000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
k divides n!.
If n is in A002981, then a(n) is - by definition - 1. If not, then none of the numbers n!+1, n!+2, ... n!+n will be prime, which gives us the lower bound a(n) > (n!+1)^n. - Stefan Steinerberger, Mar 14 2006
|
|
LINKS
|
|
|
EXAMPLE
|
a(4) = 25*26*27*28 =491400.
|
|
MATHEMATICA
|
Table[Product[i, {i, n! + 1, Prime[PrimePi[n! ] + 1] - 1}], {n, 1, 8}] (* Stefan Steinerberger, Mar 14 2006 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|