

A075054


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


2



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
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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: A079867 A079869 A200322 * A158366 A101916 A100771
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



