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A204993
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Negative of the discriminant of quadratic field Q(sqrt(-n)).
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2
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4, 8, 3, 4, 20, 24, 7, 8, 4, 40, 11, 3, 52, 56, 15, 4, 68, 8, 19, 20, 84, 88, 23, 24, 4, 104, 3, 7, 116, 120, 31, 8, 132, 136, 35, 4, 148, 152, 39, 40, 164, 168, 43, 11, 20, 184, 47, 3, 4, 8, 51, 52, 212, 24, 55, 56, 228, 232, 59, 15, 244, 248, 7, 4, 260
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OFFSET
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1,1
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COMMENTS
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For the discriminant of the quadratic field Q(sqrt(n)), see A037449.
a(n) is the smallest positive N such that ((-n)/k) = ((-n)/(k mod N)) for every odd k that is coprime to n, where ((-n)/k) is the Jacobi symbol. As we have Dirichlet's theorem on arithmetic progressions, a(n) is also the smallest positive N such that ((-n)/p) = ((-n)/(p mod N)) for every odd prime p that is not a factor of n. - Jianing Song, May 16 2024
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LINKS
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FORMULA
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Let b(n) = A007913(n), then a(n) = b(n) if b(n) == 3 (mod 4) and 4*b(n) otherwise. - Jianing Song, May 16 2024
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MATHEMATICA
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-Table[NumberFieldDiscriminant[Sqrt[-n]], {n, 1, 70}]
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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