A236208 Numbers not divisible by 2, 5 or 11.

1, 3, 7, 9, 13, 17, 19, 21, 23, 27, 29, 31, 37, 39, 41, 43, 47, 49, 51, 53, 57, 59, 61, 63, 67, 69, 71, 73, 79, 81, 83, 87, 89, 91, 93, 97, 101, 103, 107, 109, 111, 113, 117, 119, 123, 127, 129, 131, 133, 137, 139, 141, 147, 149, 151, 153, 157, 159, 161, 163

Offset: 1

Author

Oleg P. Kirillov, Jan 20 2014

Keywords

• nonn
• easy

Comments

Numbers coprime to 110. The asymptotic density of this sequence is 4/11. - Amiram Eldar, Oct 23 2020

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1).

Crossrefs

Cf. A007775, A235583, A236204.

Programs

Mathematica

Select[Range[200], CoprimeQ[110, #] &] (* Amiram Eldar, Oct 23 2020 *)

Formula

G.f.: (x^36 +x^35 +2*x^34 -2*x^33 +2*x^32 +x^31 -x^30 +2*x^29 -2*x^28 +4*x^27 -x^26 -x^25 +6*x^24 -6*x^23 +4*x^22 -x^21 +x^20 +4*x^19 -6*x^18 +4*x^17 +x^16 -x^15 +4*x^14 -6*x^13 +6*x^12 -x^11 -x^10 +4*x^9 -2*x^8 +2*x^7 -x^6 +x^5 +2*x^4 -2*x^3 +2*x^2 +x +1)*x / ((x+1) *(x^2+1) *(x^4-x^3+x^2-x+1) *(x^4+1) *(x^8-x^6+x^4-x^2+1) *(x^16-x^12+x^8-x^4+1) *(x-1)^2). - Alois P. Heinz, Feb 13 2014