A075054 Smallest k such that (n+1)(n+2)...(n+k) is divisible by n!.

1, 2, 3, 4, 5, 4, 7, 8, 9, 10, 11, 12, 13, 14, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 26, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 40, 43, 44, 43, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 64, 67, 68, 69, 70, 71, 72

Offset: 1

Author

Amarnath Murthy, Sep 07 2002

Keywords

• nonn

Comments

a(n) <= n. a(n) < n rarely, e.g. for n = 6, 15 etc. a(p) = p, p is a prime.

Examples

			a(6) = 4 as 7*8*9*10 is divisible by 6!= 720.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A075055, A058008.

Programs

Mathematica

dnf[n_]:=Module[{nf=n!,k=1},While[!Divisible[Times@@Range[ n+1,n+k],nf],k++];k]; Array[dnf,80] (* Harvey P. Dale, Jun 19 2012 *)

Extensions

More terms from Sascha Kurz, Feb 02 2003

Edited by Charles R Greathouse IV, Aug 02 2010