A075366 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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.