A075366 Smallest product (n+1)(n+2)...(n+k) that is divisible by the product of all the primes up to n.

1, 12, 120, 30, 30240, 5040, 17297280, 2162160, 240240, 360360, 28158588057600, 2346549004800, 64764752532480000, 4626053752320000, 308403583488000, 19275223968000, 830034394580628357120000, 46113021921146019840000

Offset: 1

Author

Amarnath Murthy, Sep 20 2002

Keywords

• nice
• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A075365, A075367, A075368.

Cf. A000040.

Programs

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

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]]

Formula

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

Extensions

Edited by Dean Hickerson, Oct 28 2002