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A063917 Smallest k such that k!!! is a multiple of n. 3

%I

%S 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,

%T 29,15,31,14,33,17,10,12,37,19,39,8,41,21,43,11,15,23,47,18,28,20,51,

%U 13,53,9,11,10,57,29,59,15,61,31,21,16,13,33,67,17,69

%N Smallest k such that k!!! is a multiple of n.

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

%H Vincenzo Librandi, <a href="/A063917/b063917.txt">Table of n, a(n) for n = 1..2000</a>

%H Anonymous, <a href="http://www.gallup.unm.edu/~smarandache/SKF.htm">Smarandache k-factorial</a>

%e 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.

%t 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 *)

%t 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 *)

%Y Cf. A007661.

%K nonn

%O 1,2

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

%E Offset changed and more terms by _Amiram Eldar_, Dec 08 2018

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Last modified August 4 12:33 EDT 2021. Contains 346447 sequences. (Running on oeis4.)