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

1,2

Links

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

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

Cf. A075365, A075367, A075368.

Cf. A000040.

Sequence in context: A289542 A075622 A153054 * A276668 A076633 A110423

Adjacent sequences: A075363 A075364 A075365 * A075367 A075368 A075369

Keyword

nice,nonn

Author

Amarnath Murthy, Sep 20 2002

Extensions

Edited by Dean Hickerson, Oct 28 2002

Status

approved