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%I #26 Apr 17 2024 03:28:46
%S 9,12,15,18,21,27,33,39,51,57,69,87,93,111,123,129,141,159,177,183,
%T 201,213,219,237,249,267,291,303,309,321,327,339,381,393,411,417,447,
%U 453,471,489,501,519,537,543,573,579,591,597,633,669,681,687,699,717,723
%N Numbers k whose largest divisor <= sqrt(k) is 3.
%C Define a sieve operation with parameter s that eliminates integers of the form s^2+s*i (i >= 0) from the set A000027 of natural numbers. The sequence lists those natural numbers that are eliminated by the sieve s=3 and cannot be eliminated by any sieve s >= 4. - _R. J. Mathar_, Jun 24 2009
%C See A161344 for more information. - _Omar E. Pol_, Jul 05 2009
%C See also the array in A163280, the main entry for this sequence. - _Omar E. Pol_, Oct 24 2009
%C Union of {12, 18, 27} and all the numbers of the form 3*p, where p is an odd prime. - _Amiram Eldar_, Apr 17 2024
%H Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polprdipi.jpg">Illustration: Divisors and pi(x)</a>.
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv06.jpg">Illustration for A008578, A161344, A161345 and A161424</a>. [From _Omar E. Pol_, Oct 24 2009]
%F Numbers k such that A033676(k)=3. - _Omar E. Pol_, Jul 05 2009
%p isA := proc(n,s) if n mod s <> 0 then RETURN(false); fi; if n/s-s >= 0 then RETURN(true); else RETURN(false); fi; end: isA161345 := proc(n) for s from 4 to n do if isA(n,s) then RETURN(false); fi; od: isA(n,3) ; end: for n from 1 to 3000 do if isA161345(n) then printf("%d,",n) ; fi; od; # _R. J. Mathar_, Jun 24 2009
%t md3Q[n_]:=Max[Select[Divisors[n],#<=Sqrt[n]&]]==3; Select[Range[800],md3Q] (* _Harvey P. Dale_, Aug 12 2013 *)
%Y Cf. A000005, A018253, A160811, A160812, A161205, A161344, A161346, A033676, A008578, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532.
%Y Third column of the array in A163280. Also, third row of array in A163990. - _Omar E. Pol_, Oct 24 2009
%K easy,nonn,changed
%O 1,1
%A _Omar E. Pol_, Jun 20 2009
%E Terms beyond a(10) from _R. J. Mathar_, Jun 24 2009
%E Definition added by _R. J. Mathar_, Jun 28 2009
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