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A235583 Numbers not divisible by 2, 5 or 7.

%I A235583 #28 Nov 27 2023 00:17:33
%S A235583 1,3,9,11,13,17,19,23,27,29,31,33,37,39,41,43,47,51,53,57,59,61,67,69,
%T A235583 71,73,79,81,83,87,89,93,97,99,101,103,107,109,111,113,117,121,123,
%U A235583 127,129,131,137,139,141,143,149,151,153,157,159,163,167,169,171,173,177,179,181,183
%N A235583 Numbers not divisible by 2, 5 or 7.
%C A235583 All primes, except 2, 5 and 7, are in this sequence. Any product of terms is also a term in the sequence. For example, a(2)a(4) = 3 * 11 = 33 = a(12). - _Alonso del Arte_, Jan 12 2014
%C A235583 In other words, numbers equivalent 1,3,9,...,69 modulo 70. This means the first differences of the sequence are 24-periodic. - _Ralf Stephan_, Jan 14 2014
%C A235583 Numbers coprime to 70. The asymptotic density of this sequence is 12/35. - _Amiram Eldar_, Oct 23 2020
%H A235583 Vincenzo Librandi, <a href="/A235583/b235583.txt">Table of n, a(n) for n = 1..1000</a>
%H A235583 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1).
%F A235583 G.f.: x*(x^22 +3*x^21 +8*x^20 +7*x^19 +x^18-2*x^17 -x^16 +5*x^15 +10*x^14 +7*x^13 -x^12 -6*x^11 -x^10 +7*x^9 +10*x^8 +5*x^7 -x^6 -2*x^5 +x^4 +7*x^3 +8*x^2 +3*x +1) / ((x+1) *(x^2+1) *(x^2+x+1) *(x^4-x^2+1) *(x^4+1) *(x^8-x^4+1) *(x-1)^2). - _Alois P. Heinz_, Jan 12 2014
%e A235583 51 = 3 * 17, and gcd(51, 70) = 1, so it is in the sequence.
%e A235583 53 is prime, so it is in the sequence.
%e A235583 55 = 5 * 11, and gcd(55, 70) = 5, so it is not in the sequence.
%t A235583 Select[Range[210], GCD[#, 70] == 1 &] (* _Alonso del Arte_, Jan 12 2014 *)
%t A235583 Select[Range[300], Mod[#, 2]>0 &&Mod[#, 5]>0 &&Mod[#, 7]>0&] (* _Vincenzo Librandi_, Feb 08 2014 *)
%Y A235583 Cf. A007775, A008364 (subsequence).
%K A235583 nonn,easy
%O A235583 1,2
%A A235583 _Oleg P. Kirillov_, Jan 12 2014