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%I #20 Mar 20 2021 10:57:06
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73
%N Power-6-free numbers: numbers whose exponents in their prime factorization are all less than 6.
%C Superset of A005117 and A067259. The first numbers not in the sequence are 64, 128, 192, 256, 320, 384, 448, 512, 576, 640, 704, 729 etc. [_R. J. Mathar_, Oct 11 2008]
%C This sequence has an asymptotic density of about 0.98270. - _David A. Corneth_, Nov 05 2017
%C From _Amiram Eldar_, Mar 20 2021: (Start)
%C The asymptotic density of this sequence is 1/zeta(6) = 1/A013664 = 945/Pi^6 = 0.9829525922...
%C The Schnirelmann density of this sequence is 6165/6272 (Orr, 1969). (End)
%H Robert Israel, <a href="/A144972/b144972.txt">Table of n, a(n) for n = 1..10000</a>
%H Richard C. Orr, <a href="https://doi.org/10.1112/jlms/s1-44.1.313">On the Schnirelmann density of the sequence of k-free integers</a>, Journal of the London Mathematical Society, Vol. 1, No. 1 (1969), pp. 313-319.
%F {n: A051903(n) <= 5}. [_R. J. Mathar_, Oct 11 2008, corrected Oct 19 2008]
%p select(n -> max(seq(f[2],f=ifactors(n)[2]))<=5, [$1..1000]); # _Robert Israel_, Nov 05 2017
%t lst={};Do[a=0;Do[If[FactorInteger[m][[n,2]]>5,a=1],{n,Length[FactorInteger[m]]}];If[a!=1,AppendTo[lst,m]],{m,2*5!}];lst
%t Select[Range[100], AllTrue[FactorInteger[#][[;; , 2]] , #1 < 6 & ] &] (* _Amiram Eldar_, Mar 20 2021 *)
%Y Subsequences: A005117, A004709, A046100, A067259, A051903.
%Y Cf. A013664
%K nonn
%O 1,2
%A _Vladimir Joseph Stephan Orlovsky_, Sep 27 2008
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