A091404 Numbers n such that genus of group Gamma_0(n) is 2.

22, 23, 26, 28, 29, 31, 37, 50

Offset

1,1

Comments

I assume it is known that there are no further terms? A reference for this would be nice.

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

Table of n, a(n) for n=1..8.

Formula

Numbers n such that A001617(n) = 2.

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], 2] // Flatten (* Jean-François Alcover, Oct 19 2018 *)

Crossrefs

Cf. A001617, A001615, A000089, A000086, A001616, A091401, A091403.

Sequence in context: A254751 A260993 A276182 * A260994 A114963 A146755

Adjacent sequences: A091401 A091402 A091403 * A091405 A091406 A091407

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Mar 02 2004

Status

approved