A075367 Smallest value of lcm(n+1, n+2, ..., n+k) (for k >= 0) that is divisible by the product of all the primes up to n.

1, 12, 60, 30, 2520, 2520, 360360, 180180, 60060, 60060, 232792560, 232792560, 26771144400, 26771144400, 26771144400, 13385572200, 144403552893600, 144403552893600, 5342931457063200, 5342931457063200, 5342931457063200

Offset: 1

Author

Amarnath Murthy, Sep 20 2002

Keywords

• nice
• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A075365, A075366, A075368.

Programs

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[1]=1; a[n_] := LCM@@Range[n+1, n+a75365[n]]

Formula

a(n) = lcm(n+1, ..., n + A075365(n)).

Extensions

Edited by Dean Hickerson, Oct 28 2002