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

1,2

Comments

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A075055, A058008.

Sequence in context: A079869 A200322 A361479 * A158366 A335834 A289321

Adjacent sequences: A075051 A075052 A075053 * A075055 A075056 A075057

Keyword

nonn

Author

Amarnath Murthy, Sep 07 2002

Extensions

More terms from Sascha Kurz, Feb 02 2003

Edited by Charles R Greathouse IV, Aug 02 2010

Status

approved