login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A074232 Positive numbers that are not 3 or 6 (mod 9). 3

%I

%S 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,

%T 34,35,36,37,38,40,41,43,44,45,46,47,49,50,52,53,54,55,56,58,59,61,62,

%U 63,64,65,67,68,70,71,72,73,74,76,77,79,80,81,82,83,85,86,88,89,90,91

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

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

%H R. D. Carmichael, <a href="http://dx.doi.org/10.1090/S0002-9904-1915-02730-8">On the representation of numbers in the form x^3+y^3+z^3-3xyz</a>, Bull. Amer. Math. Soc. 22 (1915), 111-117.

%H Vladimir Shevelev, <a href="http://arxiv.org/abs/1508.05748">Representation of positive integers by the form x^3+y^3+z^3-3xyz</a>, arXiv:1508.05748 [math.NT], 2015.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).

%F 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

%t Select[Range@ 91, ! Xor[Mod[#, 3] == 0, Mod[#, 9] == 0] &] (* or *)

%t Select[Range@ 91, KroneckerSymbol[#, 9] == MoebiusMu[GCD[#, 9]] &] (* _Michael De Vlieger_, Sep 07 2015 *)

%o (PARI) lista(nn) = for (n=1, nn, if (kronecker(9,n)==moebius(gcd(9,n)) , print1(n, ", "))); \\ _Michel Marcus_, Aug 12 2015

%o (PARI) is(n)=valuation(n,3)!=1 \\ _Charles R Greathouse IV_, Aug 12 2015

%Y Complement of A016051.

%K nonn,easy

%O 1,2

%A _Jon Perry_, Sep 17 2002

%E Offset corrected by _Michel Marcus_, Aug 12 2015

%E Definition edited by _N. J. A. Sloane_, Aug 25 2015

%E Better name from _Vladimir Shevelev_, Aug 12 2015

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 2 12:06 EST 2021. Contains 341750 sequences. (Running on oeis4.)