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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A029937 Genus of modular curve X_1(n). 5
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2, 5, 2, 7, 3, 5, 6, 12, 5, 12, 10, 13, 10, 22, 9, 26, 17, 21, 21, 25, 17, 40, 28, 33, 25, 51, 25, 57, 36, 41, 45, 70, 37, 69, 48, 65, 55, 92, 52, 81, 61, 85, 78, 117, 57, 126, 91, 97 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,13

COMMENTS

Also the dimension of the space of cusp forms of weight two on Gamma1(n). [Steven Finch, Apr 03 2009]

REFERENCES

F. Hirzebruch et al., Manifolds and Modular Forms, Vieweg, 2nd ed. 1994, p. 161.

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

S. R. Finch, Modular forms on SL_2(Z), December 28, 2005. [Cached copy, with permission of the author]

Chang Heon Kim, Ja Kyung Koo, On the genus of some modular curves of level N, Bull Austral. Math. Soc. 54 (1996) 291-297.

A. V. Sutherland, Torsion subgroups of elliptic curves over number fields, 2012. - From N. J. A. Sloane, Feb 03 2013

FORMULA

a(n) = 1+A115000(n)-A029935(n)/4, n>4. [Kim and Koo, Theorem 1]

MAPLE

with(numtheory); A029937 := proc(n) local i, j; j := 1+(1/24)*phi(n)*A001615(n); for i in divisors(n) do j := j-(1/4)*phi(i)*phi(n/i) od; j; end;

MATHEMATICA

a[n_ /; n<5] = 0; a[n_] := 1+Sum[d^2*MoebiusMu[n/d]/24 - EulerPhi[d]*EulerPhi[n/d]/4, {d, Divisors[n]}]; Table[a[n], {n, 1, 100}] (* Jean-Fran├žois Alcover, Jan 13 2014 *)

PROG

(PARI)

A029935(n) = {

  my(f = factor(n), fsz = matsize(f)[1],

     g = prod(k=1, fsz, f[k, 1]),

     h = prod(k=1, fsz, sqr(f[k, 1]-1)*f[k, 2] + sqr(f[k, 1])-1));

  return(h*n\sqr(g));

};

a(n) = {

  if (n < 5, return(0));

  my(f = factor(n), fsz = matsize(f)[1],

     g = prod(k=1, fsz, f[k, 1]),

     h = prod(k=1, fsz, sqr(f[k, 1]) - 1));

  return(1 + sqr(n\g)*h/24 - A029935(n)/4);

};

vector(63, n, a(n))  \\ Gheorghe Coserea, Oct 23 2016

CROSSREFS

Cf. A001617, A029938. [Steven Finch, Apr 03 2009]

Sequence in context: A336878 A305313 A159046 * A289772 A283615 A216396

Adjacent sequences:  A029934 A029935 A029936 * A029938 A029939 A029940

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

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 December 2 19:12 EST 2020. Contains 338891 sequences. (Running on oeis4.)