A161345 Numbers k whose largest divisor <= sqrt(k) is 3.

9, 12, 15, 18, 21, 27, 33, 39, 51, 57, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 201, 213, 219, 237, 249, 267, 291, 303, 309, 321, 327, 339, 381, 393, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597, 633, 669, 681, 687, 699, 717, 723

Offset: 1

Author

Omar E. Pol, Jun 20 2009

Keywords

• easy
• nonn

Comments

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

See A161344 for more information. - Omar E. Pol, Jul 05 2009

See also the array in A163280, the main entry for this sequence. - Omar E. Pol, Oct 24 2009

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

Links

• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
• Omar E. Pol, Illustration: Divisors and pi(x).
• Omar E. Pol, Illustration for A008578, A161344, A161345 and A161424. [From _Omar E. Pol_, Oct 24 2009]

Crossrefs

Cf. A000005, A018253, A160811, A160812, A161205, A161344, A161346, A033676, A008578, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532.

Third column of the array in A163280. Also, third row of array in A163990. - Omar E. Pol, Oct 24 2009

Programs

Maple

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

Mathematica

md3Q[n_]:=Max[Select[Divisors[n],#<=Sqrt[n]&]]==3; Select[Range[800],md3Q] (* Harvey P. Dale, Aug 12 2013 *)

Formula

Numbers k such that A033676(k)=3. - Omar E. Pol, Jul 05 2009

Extensions

Terms beyond a(10) from R. J. Mathar, Jun 24 2009

Definition added by R. J. Mathar, Jun 28 2009