

A074231


Numbers n such that Kronecker(8,n) = mu(gcd(8,n)).


1



1, 4, 7, 8, 9, 12, 15, 16, 17, 20, 23, 24, 25, 28, 31, 32, 33, 36, 39, 40, 41, 44, 47, 48, 49, 52, 55, 56, 57, 60, 63, 64, 65, 68, 71, 72, 73, 76, 79, 80, 81, 84, 87, 88, 89, 92, 95, 96, 97, 100, 103, 104, 105, 108, 111, 112, 113, 116, 119, 120, 121, 124, 127, 128, 129
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OFFSET

1,2


COMMENTS

A Chebyshev transform of (1+2x)/(12x) (A046055) given by G(x)>(1/(1+x^2))G(x/(1+x^2)).  Paul Barry, Oct 27 2004


LINKS

Table of n, a(n) for n=1..65.


FORMULA

From Paul Barry, Oct 27 2004: (Start)
G.f.: (1+x)^2/((1+x^2)*(12x+x^2));
e.g.f.: exp(x)(2+2x)  cos(x);
a(n) = 2n + 2  cos(Pi*n/2);
a(n) = Sum_{k=0..n} (0^k + 4^k)*cos(Pi*(nk)/2);
a(n) = Sum_{k=0..floor(n/2)} C(nk, k)*(1)^k(2*2^(n2k)0^(n2k));
a(n) = 2a(n1)  2a(n2) + 2a(n3)  a(n4). (End)


PROG

(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)))))
(Sage) [lucas_number1(n+2, 0, 1)+2*n for n in range(1, 66)] # Zerinvary Lajos, Mar 09 2009


CROSSREFS

Essentially the same as A047538.
Sequence in context: A253472 A255060 A047538 * A310938 A289631 A076680
Adjacent sequences: A074228 A074229 A074230 * A074232 A074233 A074234


KEYWORD

nonn


AUTHOR

Jon Perry, Sep 17 2002


STATUS

approved



