

A086227


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


1



1, 2, 2, 2, 4, 4, 4, 6, 4, 6, 8, 6, 8, 8, 8, 8, 12, 10, 8, 16, 12, 12, 16, 10, 12, 18, 16, 14, 16, 16, 16, 24, 16, 16, 24, 18, 20, 24, 16, 20, 32, 22, 24, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,2


COMMENTS

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


LINKS

Table of n, a(n) for n=2..78.


PROG

(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)))))
(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
(PARI) a(n)=my(s); for(k=1, 2*n, if(gcd(2*k1, n)==1, s=(1)^k*tan((2*k1)*Pi/4/n))); round(s/4) \\ Charles R Greathouse IV, Apr 25 2013


CROSSREFS

Sequence in context: A240321 A054861 A187324 * A079438 A123050 A113694
Adjacent sequences: A086224 A086225 A086226 * A086228 A086229 A086230


KEYWORD

sign


AUTHOR

Benoit Cloitre, Aug 28 2003


EXTENSIONS

Definition corrected by Charles R Greathouse IV, Apr 25 2013


STATUS

approved



