A235583 -id:A235583 - cp's OEIS frontend

A236204 Numbers not divisible by 2, 3 or 11.

1, 5, 7, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 59, 61, 65, 67, 71, 73, 79, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 125, 127, 131, 133, 137, 139, 145, 149, 151, 155, 157, 161, 163, 167, 169, 173, 175, 179, 181, 185, 191, 193, 197, 199, 203, 205

Offset: 1

Oleg P. Kirillov, Jan 20 2014

All primes except 2, 3 and 11 are in this sequence. Any product of terms is also a term in the sequence. - Alonso del Arte, Feb 04 2014
Also integers n such that least prime factor of 32^n-1 is 31. - Giovanni Resta, Mar 22 2014
Numbers coprime to 66. The asymptotic density of this sequence is 10/33. - Amiram Eldar, Oct 23 2020

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

Cf. A235583.

Select[2Range[125] - 1, GCD[#, 66] == 1 &] (* Alonso del Arte, Feb 04 2014 *)

is(n)=gcd(n,66)==1 \\ Charles R Greathouse IV, Mar 26 2014

a(n) = a(n-1) + a(n-20) - a(n-21). - Charles R Greathouse IV, Mar 26 2014
For n > 20, a(n) = a(n - 20) + 66. - Zak Seidov, Mar 27 2014
G.f.: x*(x^20 + 4*x^19 + 2*x^18 + 6*x^17 + 4*x^16 + 2*x^15 + 4*x^14 + 2*x^13 + 4*x^12 + 2*x^11 + 4*x^10 + 2*x^9 + 4*x^8 + 2*x^7 + 4*x^6 + 2*x^5 + 4*x^4 + 6*x^3 + 2*x^2 + 4*x + 1)/(x^21 - x^20 - x + 1). - Chai Wah Wu, Aug 03 2020

A236208 Numbers not divisible by 2, 5 or 11.

Original entry on oeis.org

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

Oleg P. Kirillov, Jan 20 2014

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

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).

Cf. A007775, A235583, A236204.

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

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

A362011 Numbers k such that 1 < gcd(k, 70) < k and A007947(k) does not divide 70.

Original entry on oeis.org

6, 12, 15, 18, 21, 22, 24, 26, 30, 34, 36, 38, 42, 44, 45, 46, 48, 52, 54, 55, 58, 60, 62, 63, 65, 66, 68, 72, 74, 75, 76, 77, 78, 82, 84, 85, 86, 88, 90, 91, 92, 94, 95, 96, 102, 104, 105, 106, 108, 110, 114, 115, 116, 118, 119, 120, 122, 124, 126, 130, 132, 133, 134, 135, 136, 138, 142, 144, 145, 146

Offset: 1

Michael De Vlieger, Apr 04 2023

nonn

The asymptotic density of this sequence is 23/35. - Amiram Eldar, Dec 02 2023

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Diagram showing numbers k in this sequence instead as k mod 70 arranged in rows, labeled and in large black circles, else gray dots if coprime to 70, purple if k = 1, red if k | 70, and gold if rad(k) | 70.

Cf. A007947, A108513, A235583.

With[{n = 70}, Select[Range[200], And[! CoprimeQ[#, n], ! Divisible[n, Times @@ FactorInteger[#][[All, 1]]]] & ] ]

This sequence is { N \ { A108513 U A235583 } }.

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A236204 Numbers not divisible by 2, 3 or 11.

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A236208 Numbers not divisible by 2, 5 or 11.

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A362011 Numbers k such that 1 < gcd(k, 70) < k and A007947(k) does not divide 70.

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