A075366 - OEIS

%I #10 May 18 2015 15:58:36

%S 1,12,120,30,30240,5040,17297280,2162160,240240,360360,28158588057600,

%T 2346549004800,64764752532480000,4626053752320000,308403583488000,

%U 19275223968000,830034394580628357120000,46113021921146019840000

%N Smallest product (n+1)(n+2)...(n+k) that is divisible by the product of all the primes up to n.

%H Reinhard Zumkeller, <a href="/A075366/b075366.txt">Table of n, a(n) for n = 1..300</a>

%F If p <= n < q, where p and q are consecutive primes, then a(n) = (2p)!/n!, unless n=10.

%t 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 (Haskell)

%o a075366 n = a075366_list !! (n-1)

%o a075366_list = 1 : f 2 1 a000040_list where

%o    f x pp ps'@(p:ps)

%o      | p <= x    = f x (p * pp) ps

%o      | otherwise = g $ dropWhile (< pp) $ scanl1 (*) [x+1, x+2 ..]

%o      where g (z:zs) | mod z pp == 0 = z : f (x + 1) pp ps'

%o                     | otherwise     = g zs

%o -- _Reinhard Zumkeller_, May 18 2015

%Y Cf. A075365, A075367, A075368.

%Y Cf. A000040.

%K nice,nonn

%O 1,2

%A _Amarnath Murthy_, Sep 20 2002

%E Edited by _Dean Hickerson_, Oct 28 2002