A074232 Positive numbers that are not 3 or 6 (mod 9).

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

Offset

1,2

Comments

Previous name was: Numbers n such that Kronecker(9,n) = mu(gcd(9,n)).

Links

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).

Formula

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

Mathematica

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 *)

Prog

(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

Crossrefs

Complement of A016051.

Sequence in context: A039184 A039137 A071807 * A007417 A039099 A215069

Adjacent sequences: A074229 A074230 A074231 * A074233 A074234 A074235

Keyword

nonn,easy

Author

Jon Perry, Sep 17 2002

Extensions

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

Status

approved