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A256945 Number of periods of reduced indefinite binary quadratic forms with discriminant D(n) = A079896(n). 1

%I

%S 1,1,2,1,1,2,2,2,2,1,3,2,1,2,1,2,3,4,2,1,2,2,4,1,2,2,2,3,1,2,2,4,4,2,

%T 2,1,2,2,6,1,1,2,4,4,1,4,1,2,3,4,2,2,5,2,4,2,4,1,4,2,4,4

%N Number of periods of reduced indefinite binary quadratic forms with discriminant D(n) = A079896(n).

%C This is an ``imprimitive'' class number. Each a(n) is A087048(n) increased by the number of cycles of discriminant D(n) of imprimitive binary quadratic forms.

%C The gcd of the coefficients is the same for each form within a cycle, so is a cycle invariant. There will exist cycles with gcd invariant equal to k precisely when D(n)/k^2 = A079896(m) for some m. In this case, the number of such cycles is A087048(m).

%F a(n) is the sum A087048(m) over all integers m with D(m)= D(n)/k^2 for some integer k.

%e a(5) gives the number of cycles of reduced indefinite forms of discriminant D(5) = 20. This is the sum A087048(0) + A087048(5) = 2.

%Y Cf. A079896, A087048.

%K nonn,more

%O 0,3

%A _Barry R. Smith_, Apr 19 2015

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Last modified October 6 16:13 EDT 2022. Contains 357269 sequences. (Running on oeis4.)