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 A091403 Numbers n such that genus of group Gamma_0(n) is 1. 5
 11, 14, 15, 17, 19, 20, 21, 24, 27, 32, 36, 49 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS I assume it is known that there are no further terms? A reference for this would be nice. Available conductors for modular elliptic curves genus 1. [From Artur Jasinski, Jun 24 2010] REFERENCES B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, p. 103. G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton, 1971, see Prop. 1.40 and 1.43. LINKS FORMULA Numbers n such that A001617(n) = 1. MATHEMATICA a89[n_] := a89[n] = Product[{p, e} = pe; Which[p < 3 && e == 1, 1, p == 2 && e > 1, 0, Mod[p, 4] == 1, 2, Mod[p, 4] == 3, 0, True, a89[p^e]], {pe, FactorInteger[n]}]; a86[n_] := a86[n] = Product[{p, e} = pe; Which[p == 1 || p == 3 && e == 1, 1, p == 3 && e > 1, 0, Mod[p, 3] == 1, 2, Mod[p, 3] == 2, 0, True, a86[p^e]], {pe, FactorInteger[n]}]; a1615[n_] := n Sum[MoebiusMu[d]^2/d, {d, Divisors[n]}]; a1616[n_] := Sum[EulerPhi[GCD[ d, n/d]], {d, Divisors[n]}]; a1617[n_] := 1 + a1615[n]/12 - a89[n]/4 - a86[n]/3 - a1616[n]/2; Position[Array[a1617, 100], 1] // Flatten (* Jean-François Alcover, Oct 18 2018 *) CROSSREFS Cf. A001617, A001615, A000089, A000086, A001616, A091401, A091404. Sequence in context: A132991 A031167 A005788 * A061743 A038630 A239935 Adjacent sequences:  A091400 A091401 A091402 * A091404 A091405 A091406 KEYWORD nonn,fini,full AUTHOR N. J. A. Sloane, Mar 02 2004 STATUS approved

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Last modified July 24 05:05 EDT 2021. Contains 346273 sequences. (Running on oeis4.)