This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A074232 #51 Jun 29 2024 06:14:45 %S A074232 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 A074232 34,35,36,37,38,40,41,43,44,45,46,47,49,50,52,53,54,55,56,58,59,61,62, %U A074232 63,64,65,67,68,70,71,72,73,74,76,77,79,80,81,82,83,85,86,88,89,90,91 %N A074232 Positive numbers that are not 3 or 6 (mod 9). %C A074232 Previous name was: Numbers n such that Kronecker(9,n) = mu(gcd(9,n)). %C A074232 From _Antti Karttunen_, Jun 28 2024: (Start) %C A074232 Numbers whose 3-adic valuation is not 1; union of non-multiples of 3 and multiples of 9. %C A074232 A multiplicative semigroup: if m and n are in the sequence, then so is m*n. %C A074232 (End) %C A074232 The asymptotic density of this sequence is 7/9. - _Amiram Eldar_, Jun 28 2024 %H A074232 Antti Karttunen, <a href="/A074232/b074232.txt">Table of n, a(n) for n = 1..12000</a> %H A074232 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 A074232 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 A074232 <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 A074232 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 A074232 Select[Range@ 91, ! Xor[Mod[#, 3] == 0, Mod[#, 9] == 0] &] (* or *) %t A074232 Select[Range@ 91, KroneckerSymbol[#, 9] == MoebiusMu[GCD[#, 9]] &] (* _Michael De Vlieger_, Sep 07 2015 *) %o A074232 (PARI) lista(nn) = for (n=1, nn, if (kronecker(9,n)==moebius(gcd(9,n)) , print1(n, ", "))); \\ _Michel Marcus_, Aug 12 2015 %o A074232 (PARI) is(n)=valuation(n,3)!=1 \\ _Charles R Greathouse IV_, Aug 12 2015 %Y A074232 Complement of A016051. %Y A074232 Disjoint union of A001651 and A008591. %Y A074232 Cf. A007949, A374039 (characteristic function). %Y A074232 Cf. A327863, A373478, A373992, A374042 (subsequences). %K A074232 nonn,easy %O A074232 1,2 %A A074232 _Jon Perry_, Sep 17 2002 %E A074232 Offset corrected by _Michel Marcus_, Aug 12 2015 %E A074232 Definition edited by _N. J. A. Sloane_, Aug 25 2015 %E A074232 Better name from _Vladimir Shevelev_, Aug 12 2015