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A086227 a(n)=Sum( i^k*tan(k*Pi/(4n)))/(4i) where 1<=k<=4n and (k,n)=1. 1

%I

%S -1,2,-2,2,-4,4,-4,6,-4,6,-8,6,-8,8,-8,8,-12,10,-8,16,-12,12,-16,10,

%T -12,18,-16,14,-16,16,-16,24,-16,16,-24,18,-20,24,-16,20,-32,22,-24,

%U 24,-24,24,-32,28,-20,32,-24,26,-36,24,-32,40,-28,30,-32,30,-32,48,-32,24,-48,34,-32,48,-32,36,-48,36,-36,40,-40,48,-48

%N a(n)=Sum( i^k*tan(k*Pi/(4n)))/(4i) where 1<=k<=4n and (k,n)=1.

%C This seems to be (-1)^(n+1) times h(-4n^2) = (-1)^(n+1)*A000003(n^2), where h(k) is the class number. Verified for n <= 10^5. - _Charles R Greathouse IV_, Apr 28 2013

%o (PARI) a(n)=round(real(1/4/I*sum(k=1,4*n,(I^k)*tan(Pi/4/n*if(gcd(k,n)-1,0,k)))))

%o (PARI) a(n)=round(imag(sum(k=1,4*n,if(gcd(k,n)==1,I^k*tan(k*Pi/4/n))))/4) \\ _Charles R Greathouse IV_, Apr 25 2013

%o (PARI) a(n)=my(s);for(k=1,2*n,if(gcd(2*k-1,n)==1,s-=(-1)^k*tan((2*k-1)*Pi/4/n))); round(s/4) \\ _Charles R Greathouse IV_, Apr 25 2013

%K sign

%O 2,2

%A _Benoit Cloitre_, Aug 28 2003

%E Definition corrected by _Charles R Greathouse IV_, Apr 25 2013

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Last modified May 21 19:18 EDT 2019. Contains 323444 sequences. (Running on oeis4.)