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A256945
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Number of periods of reduced indefinite binary quadratic forms with discriminant D(n) = A079896(n).
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1
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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, 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
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OFFSET
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0,3
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COMMENTS
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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.
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).
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LINKS
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FORMULA
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a(n) is the sum A087048(m) over all integers m with D(m)= D(n)/k^2 for some integer k.
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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