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Largest 3-smooth number <= n.
1

%I #13 Oct 14 2021 15:57:42

%S 1,2,3,4,4,6,6,8,9,9,9,12,12,12,12,16,16,18,18,18,18,18,18,24,24,24,

%T 27,27,27,27,27,32,32,32,32,36,36,36,36,36,36,36,36,36,36,36,36,48,48,

%U 48,48,48,48,54,54,54,54,54,54,54,54,54,54,64,64,64,64,64,64,64,64,72,72

%N Largest 3-smooth number <= n.

%H David A. Corneth, <a href="/A179276/b179276.txt">Table of n, a(n) for n = 1..10000</a>

%F A065333(a(n)) = 1;

%F a(A003586(n)) = A003586(n);

%F A065331(n) <= a(n).

%t smooth3Q[n_] := FactorInteger[n][[-1, 1]] <= 3;

%t a[n_] := For[k = n, True, k--, If[smooth3Q[k], Return[k]]];

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Oct 14 2021 *)

%Y Cf. A003586, A065331, A065333, A081328.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jul 07 2010

%E Definition corrected by _Georg Fischer_, Aug 05 2021