A080671 - OEIS

%I #39 Sep 22 2024 15:19:57

%S 2,3,4,5,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,

%T 35,36,38,39,40,42,44,45,46,48,50,51,52,54,55,56,57,58,60,62,63,64,65,

%U 66,68,69,70,72,74,75,76,78,80,81,82,84,85,86,87,88,90,92,93,94,95,96,98

%N Numbers having divisors 2 or 3 or 5.

%C Complement of A007775. - _Gary Detlefs_, Oct 06 2013

%C The asymptotic density of this sequence is 11/15. - _Amiram Eldar_, Dec 07 2020

%H N. J. A. Sloane, <a href="/A080671/b080671.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-1).

%F a(n+22) = a(n) + 30. - _Gary Detlefs_, Oct 06 2013

%F G.f.: x *( 2 -x +2*x^2 -x^3 +2*x^4 +x^6 +2*x^8 +x^10 +2*x^12 +x^14 +2*x^16 -x^17 +2*x^18 -x^19 +2*x^20 ) / ( (x^10 -x^9 +x^8 -x^7 +x^6 -x^5 +x^4 -x^3 +x^2 -x+1)*(1 +x +x^5 +x^6 +x^7 +x^8 +x^9 +x^2 +x^4 +x^3 +x^10)*(x-1)^2 ). - _R. J. Mathar_, Jul 11 2024

%F Union of A281746 and A005843, without {0}. - _R. J. Mathar_, Jul 11 2024

%p A080671 := proc(n) local s; option remember;

%p s:=[2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30];

%p if n <= 22 then s[n] else 30 + A080671(n-22); fi; end proc; # _N. J. A. Sloane_, Sep 01 2022

%t Select[Range[98], Mod[#, 2]*Mod[#, 3]*Mod[#, 5] == 0 &] (* _T. D. Noe_, Oct 07 2013 *)

%t d235Q[n_]:=AnyTrue[Divisors[n],MemberQ[{2,3,5},#]&]; Select[Range[100],d235Q] (* _Harvey P. Dale_, Sep 22 2024 *)

%o (PARI) div235(n) = { for(x=1,n, if(gcd(x,30)<>1,print1(x", ")) ) }

%Y Cf. A005843, A007775, A281746 (divisors 3 or 5).

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Mar 02 2003