A080671 Numbers having divisors 2 or 3 or 5.

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, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 98

Offset: 1

Author

Cino Hilliard, Mar 02 2003

Keywords

• easy
• nonn

Comments

Complement of A007775. - Gary Detlefs, Oct 06 2013

The asymptotic density of this sequence is 11/15. - Amiram Eldar, Dec 07 2020

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-1).

Crossrefs

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

Programs

Maple

A080671 := proc(n) local s; option remember;
s:=[2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30];
if n <= 22 then s[n] else 30 + A080671(n-22); fi; end proc; # N. J. A. Sloane, Sep 01 2022

Mathematica

Select[Range[98], Mod[#, 2]*Mod[#, 3]*Mod[#, 5] == 0 &] (* T. D. Noe, Oct 07 2013 *)
d235Q[n_]:=AnyTrue[Divisors[n],MemberQ[{2,3,5},#]&]; Select[Range[100],d235Q] (* Harvey P. Dale, Sep 22 2024 *)

PARI

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

Formula

a(n+22) = a(n) + 30. - Gary Detlefs, Oct 06 2013

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

Union of A281746 and A005843, without {0}. - R. J. Mathar, Jul 11 2024