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A047304
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Numbers not divisible by 7.
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10
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1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66
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OFFSET
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1,2
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COMMENTS
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Numbers that are congruent to {1, 2, 3, 4, 5, 6} mod 7. Different from A020658.
More generally the sequence of numbers not divisible by some fixed integer m >= 2 is given by a(n,m) = n - 1 + floor((n+m-2)/(m-1)). - Benoit Cloitre, Jul 11 2009
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LINKS
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FORMULA
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G.f.: x*(1+x+x^2+x^3+x^4+x^5+x^6) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
Sum_{n>=1} (-1)^(n+1)/a(n) = (cot(Pi/7) + tan(Pi/14) - tan(3*Pi/14))*Pi/7. - Amiram Eldar, Dec 31 2021
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MATHEMATICA
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Drop[Range[70], {7, -1, 7}] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {1, 2, 3, 4, 5, 6, 8}, 60] (* Harvey P. Dale, Aug 01 2021 *)
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PROG
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(Sage) [i for i in range(67) if gcd(7, i) == 1] # Zerinvary Lajos, Apr 21 2009
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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