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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.

%I A075366 #10 May 18 2015 15:58:36
%S A075366 1,12,120,30,30240,5040,17297280,2162160,240240,360360,28158588057600,
%T A075366 2346549004800,64764752532480000,4626053752320000,308403583488000,
%U A075366 19275223968000,830034394580628357120000,46113021921146019840000
%N A075366 Smallest product (n+1)(n+2)...(n+k) that is divisible by the product of all the primes up to n.
%H A075366 Reinhard Zumkeller, <a href="/A075366/b075366.txt">Table of n, a(n) for n = 1..300</a>
%F A075366 If p <= n < q, where p and q are consecutive primes, then a(n) = (2p)!/n!, unless n=10.
%t A075366 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]]
%o A075366 (Haskell)
%o A075366 a075366 n = a075366_list !! (n-1)
%o A075366 a075366_list = 1 : f 2 1 a000040_list where
%o A075366    f x pp ps'@(p:ps)
%o A075366      | p <= x    = f x (p * pp) ps
%o A075366      | otherwise = g $ dropWhile (< pp) $ scanl1 (*) [x+1, x+2 ..]
%o A075366      where g (z:zs) | mod z pp == 0 = z : f (x + 1) pp ps'
%o A075366                     | otherwise     = g zs
%o A075366 -- _Reinhard Zumkeller_, May 18 2015
%Y A075366 Cf. A075365, A075367, A075368.
%Y A075366 Cf. A000040.
%K A075366 nice,nonn
%O A075366 1,2
%A A075366 _Amarnath Murthy_, Sep 20 2002
%E A075366 Edited by _Dean Hickerson_, Oct 28 2002