login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A091404 Numbers n such that genus of group Gamma_0(n) is 2. 4
22, 23, 26, 28, 29, 31, 37, 50 (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.

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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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