A074229 Numbers n such that Kronecker(6,n)==mu(gcd(6,n)).

1, 5, 19, 23, 25, 29, 43, 47, 49, 53, 67, 71, 73, 77, 91, 95, 97, 101, 115, 119, 121, 125, 139, 143, 145, 149, 163, 167, 169, 173, 187, 191, 193, 197, 211, 215, 217, 221, 235, 239, 241, 245, 259, 263, 265, 269, 283, 287, 289, 293, 307, 311, 313, 317, 331, 335

Offset: 1

Author

Jon Perry, Sep 17 2002

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Equals 2 * A072065 + 1.

Programs

PARI

for (x=1,200, for (y=1,200,if (kronecker(x,y)==moebius(gcd(x,y)),write("km.txt",x,";",y," : ",kronecker(x,y)))))

PARI

isok(n) = kronecker(6, n) == moebius(gcd(6, n)); \\ Michel Marcus, Mar 17 2014

PARI

Vec(x*(1+4*x+14*x^2+4*x^3+x^4)/((1-x)^2*(1+x)*(1+x^2)) + O(x^100)) \\ Colin Barker, Dec 14 2015

Formula

From Colin Barker, Dec 14 2015: (Start)

a(n) = (3/2+(3*i)/2)*(i^n-i*(-i)^n)-(-1)^n+6*(n+1)-9 where i = sqrt(-1).

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

G.f.: x*(1+4*x+14*x^2+4*x^3+x^4) / ((1-x)^2*(1+x)*(1+x^2)).

(End)

Extensions

More terms from Michel Marcus, Mar 17 2014