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A074232
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Positive numbers that are not 3 or 6 (mod 9).
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3
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1, 2, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 20, 22, 23, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, 37, 38, 40, 41, 43, 44, 45, 46, 47, 49, 50, 52, 53, 54, 55, 56, 58, 59, 61, 62, 63, 64, 65, 67, 68, 70, 71, 72, 73, 74, 76, 77, 79, 80, 81, 82, 83, 85, 86, 88, 89, 90, 91
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OFFSET
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1,2
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COMMENTS
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Previous name was: Numbers n such that Kronecker(9,n) = mu(gcd(9,n)).
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LINKS
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Table of n, a(n) for n=1..71.
R. D. Carmichael, On the representation of numbers in the form x^3+y^3+z^3-3xyz, Bull. Amer. Math. Soc. 22 (1915), 111-117.
Vladimir Shevelev, Representation of positive integers by the form x^3+y^3+z^3-3xyz, arXiv:1508.05748 [math.NT], 2015.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).
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FORMULA
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G.f.: x*(x^2-x+1)*(1+x+x^2)^2 / ( (x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Apr 28 2016
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MATHEMATICA
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Select[Range@ 91, ! Xor[Mod[#, 3] == 0, Mod[#, 9] == 0] &] (* or *)
Select[Range@ 91, KroneckerSymbol[#, 9] == MoebiusMu[GCD[#, 9]] &] (* Michael De Vlieger, Sep 07 2015 *)
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PROG
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(PARI) lista(nn) = for (n=1, nn, if (kronecker(9, n)==moebius(gcd(9, n)) , print1(n, ", "))); \\ Michel Marcus, Aug 12 2015
(PARI) is(n)=valuation(n, 3)!=1 \\ Charles R Greathouse IV, Aug 12 2015
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CROSSREFS
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Complement of A016051.
Sequence in context: A039184 A039137 A071807 * A007417 A039099 A215069
Adjacent sequences: A074229 A074230 A074231 * A074233 A074234 A074235
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KEYWORD
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nonn,easy
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AUTHOR
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Jon Perry, Sep 17 2002
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EXTENSIONS
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Offset corrected by Michel Marcus, Aug 12 2015
Definition edited by N. J. A. Sloane, Aug 25 2015
Better name from Vladimir Shevelev, Aug 12 2015
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STATUS
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approved
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