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A112347 Kronecker symbol (-1, n) except a(0) = 0. 0

%I

%S 0,1,1,-1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1,

%T -1,1,-1,-1,1,1,1,-1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,

%U -1,-1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,-1

%N Kronecker symbol (-1, n) except a(0) = 0.

%F Multiplicative with a(2^e) = 1, a(p^e) = (-1)^(e(p-1)/2) if p>2.

%F a(2n) = a(n), a(4*n + 1) = 1, a(4*n + 3) = -1. a(-n) = -a(n).

%F a(n) = A034947(n) unless n=0.

%e x + x^2 - x^3 + x^4 + x^5 - x^6 - x^7 + x^8 + x^9 + x^10 - x^11 - x^12 + x^13 + ...

%t Join[{0},KroneckerSymbol[-1,Range[110]]] (* _Harvey P. Dale_, Jun 02 2019 *)

%o (PARI) {a(n) = if( n, kronecker( -1, n))}

%Y Cf. A034947.

%K sign,mult

%O 0,1

%A _Michael Somos_, Sep 12 2005

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Last modified June 7 02:48 EDT 2020. Contains 334836 sequences. (Running on oeis4.)