

A235583


Numbers not divisible by 2, 5 or 7.


4



1, 3, 9, 11, 13, 17, 19, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 51, 53, 57, 59, 61, 67, 69, 71, 73, 79, 81, 83, 87, 89, 93, 97, 99, 101, 103, 107, 109, 111, 113, 117, 121, 123, 127, 129, 131, 137, 139, 141, 143, 149, 151, 153, 157, 159, 163, 167, 169, 171, 173, 177, 179, 181, 183
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OFFSET

1,2


COMMENTS

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
In other words, numbers equivalent 1,3,9,...,69 modulo 70. This means the first differences of the sequence are 24periodic.  Ralf Stephan, Jan 14 2014
Numbers coprime to 70. The asymptotic density of this sequence is 12/35.  Amiram Eldar, Oct 23 2020


LINKS

Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1).


FORMULA

G.f.: x*(x^22 +3*x^21 +8*x^20 +7*x^19 +x^182*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^4x^2+1) *(x^4+1) *(x^8x^4+1) *(x1)^2).  Alois P. Heinz, Jan 12 2014


EXAMPLE

51 = 3 * 17, and gcd(51, 70) = 1, so it is in the sequence.
53 is prime, so it is in the sequence.
55 = 5 * 11, and gcd(55, 70) = 5, so it is not in the sequence.


MATHEMATICA

Select[Range[300], Mod[#, 2]>0 &&Mod[#, 5]>0 &&Mod[#, 7]>0&] (* Vincenzo Librandi, Feb 08 2014 *)


CROSSREFS



KEYWORD

nonn,easy,changed


AUTHOR



STATUS

approved



