A063917 Smallest k such that k!!! is a multiple of n.

1, 2, 3, 4, 5, 6, 7, 8, 6, 5, 11, 12, 13, 7, 15, 8, 17, 6, 19, 8, 21, 11, 23, 12, 20, 13, 9, 7, 29, 15, 31, 14, 33, 17, 10, 12, 37, 19, 39, 8, 41, 21, 43, 11, 15, 23, 47, 18, 28, 20, 51, 13, 53, 9, 11, 10, 57, 29, 59, 15, 61, 31, 21, 16, 13, 33, 67, 17, 69

Offset: 1

Author

Mike Antholy (mikeantholy(AT)yahoo.ca), Aug 31 2001

Keywords

• nonn

Examples

			a(16) = 8 because 8!!! = 8*(8 - 3)*(8 - 6) = 8*5*2 which is divisible by 16 and 8 is the smallest integer with this property.
		

References

• F. Smarandache, "Some problems in number theory", Student Conference, University of Craiova, Department of Mathematics, 1979.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000
• Anonymous, Smarandache k-factorial

Crossrefs

Cf. A007661.

Programs

Mathematica

f[n_] := Product[k, {k, n, 1, -3}]; a[n_] := Module[{k = 1}, While[! Divisible[ f[k], n], k++]; k]; Array[a, 100]  (* Amiram Eldar, Dec 08 2018 *)
With[{tbl=Table[Times@@Range[k,1,-3],{k,100}]},Table[Position[tbl,?(Divisible[ #,n]&),1,1],{n,70}]]//Flatten (* _Harvey P. Dale, Feb 11 2020 *)

Extensions

Offset changed and more terms by Amiram Eldar, Dec 08 2018