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A075366
Smallest product (n+1)(n+2)...(n+k) that is divisible by the product of all the primes up to n.
4
1, 12, 120, 30, 30240, 5040, 17297280, 2162160, 240240, 360360, 28158588057600, 2346549004800, 64764752532480000, 4626053752320000, 308403583488000, 19275223968000, 830034394580628357120000, 46113021921146019840000
OFFSET
1,2
LINKS
FORMULA
If p <= n < q, where p and q are consecutive primes, then a(n) = (2p)!/n!, unless n=10.
MATHEMATICA
a75365[n_] := Module[{div, k, pr}, div=Times@@Prime/@Range[PrimePi[n]]; For[k=0; pr=1, True, k++; pr*=n+k, If[Mod[pr, div]==0, Return[k]]]]; a[n_] := Times@@Range[n+1, n+a75365[n]]
PROG
(Haskell)
a075366 n = a075366_list !! (n-1)
a075366_list = 1 : f 2 1 a000040_list where
f x pp ps'@(p:ps)
| p <= x = f x (p * pp) ps
| otherwise = g $ dropWhile (< pp) $ scanl1 (*) [x+1, x+2 ..]
where g (z:zs) | mod z pp == 0 = z : f (x + 1) pp ps'
| otherwise = g zs
-- Reinhard Zumkeller, May 18 2015
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
Amarnath Murthy, Sep 20 2002
EXTENSIONS
Edited by Dean Hickerson, Oct 28 2002
STATUS
approved