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A091401
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Numbers n such that genus of group Gamma_0(n) is zero.
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22
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 16, 18, 25
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OFFSET
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1,2
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COMMENTS
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Equivalently, numbers n such that genus of modular curve X_0(n) is zero.
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REFERENCES
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G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton, 1971, see Prop. 1.40 and 1.43.
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LINKS
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FORMULA
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Numbers n such that A001617(n) = 0.
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MATHEMATICA
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Flatten@ Position[#, 0] &@ Table[If[n < 1, 0, 1 + Sum[MoebiusMu[d]^2 n/d/12 - EulerPhi[GCD[d, n/d]]/2, {d, Divisors@ n}] - Count[(#^2 - # + 1)/n & /@ Range@ n, _?IntegerQ]/3 - Count[(#^2 + 1)/n & /@ Range@ n, _?IntegerQ]/4], {n, 120}] (* Michael De Vlieger, Dec 05 2016, after Michael Somos at A001617 *)
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CROSSREFS
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The table below is a consequence of Theorem 7.3 in Maier's paper.
N EntryID K alpha
1
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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