A093886 Least k such that k! is divisible by (1!*2!*3!*...*n!).

1, 2, 4, 8, 10, 16, 18, 26, 32, 40, 48, 60, 68, 80, 92, 108, 124, 136, 154, 172, 192, 208, 228, 252, 272, 296, 320, 344, 368, 394, 420, 452, 484, 512, 544, 580, 616, 648, 686, 724, 764, 800, 840, 880, 922, 964, 1008, 1050, 1096, 1144, 1192, 1240, 1288, 1340

Offset

1,2

Comments

k < n(n+1)/2 as n! divides every product of n successive integers.

Links

Table of n, a(n) for n=1..54.

Example

a(4) = 8 as 1!*2!*3!*4! = 288 divides 8!= 40320 but not 7! = 5040.

Maple

a:=proc(n) local A, k: A:={}: for k from 1 to n*(n+1)/2 do if type(k!/product(j!, j=1..n), integer)=true then A:=A union {k} else A:=A fi od: A[1]; end: seq(a(n), n=1..60); # not necessarily the best Maple program # Emeric Deutsch, Feb 03 2006

Mathematica

lkprmrl[n_]:=Module[{k=1}, While[Mod[k!, n]!=0, k++]; k]; Module[{nn = 60, prmrl}, prmrl = FoldList[ Times, Range[nn]!]; lkprmrl/@prmrl] (* Harvey P. Dale, Mar 25 2023 *)

Crossrefs

Cf. A093887.

Sequence in context: A369492 A339608 A268497 * A352203 A125732 A032533

Adjacent sequences: A093883 A093884 A093885 * A093887 A093888 A093889

Keyword

nonn

Author

Amarnath Murthy, Apr 23 2004

Extensions

More terms from Emeric Deutsch, Feb 03 2006

Status

approved