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%I #13 Jan 18 2024 07:47:04
%S 0,0,0,1,1,0,2,0,0,0,2,0,3,0,0,0,3,0,4,0,0,0,4,0,0,0,0,0,4,0,8,0,0,0,
%T 0,0,9,0,0,0,6,0,10,0,0,0,8,0,0,0,0,0,9,0,0,0,0,0,8,0,15,0,0,0,0,0,16,
%U 0,0,0,12,0,18,0,0,0,0,0,16,0,0,0,12,0,0,0,0,0,12,0,0,0,0,0,0,0,21,0,0,0,16
%N a(n) = number of nonexistent values of cos(2*Pi/k) mod n, taken over k = 1..n-1.
%C See A164823 for explanatory comment and the definition of "cos(x) mod j".
%C It appears that a(n) = 0 for all n >= 1 other than n = 4 and n = any prime >= 5. Also, a(n) is even for all primes of the form 4m+3, with m >= 1, since, referring to the triangle in A165609, if c mod n is nonexistent then so is -c mod n.
%H Christopher Hunt Gribble, <a href="/A165619/b165619.txt">Table of n, a(n) for n = 1..1000</a>.
%Y Cf. A164823, A165609.
%K nonn
%O 1,7
%A _Christopher Hunt Gribble_, Sep 22 2009
%E Comment corrected by _Christopher Hunt Gribble_, Sep 25 2009