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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A054728 a(n) is the smallest level N such that genus of modular curve X_0(N) is n (or -1 if no such curve exists). 4
 1, 11, 22, 30, 38, 42, 58, 60, 74, 66, 86, 78, 106, 105, 118, 102, 134, 114, 223, 132, 166, 138, 188, 156, 202, 168, 214, 174, 236, 186, 359, 204, 262, 230, 278, 222, 298, 240, 314, 246, 326, 210, 346, 270, 358, 282, 557, 306, 394, 312, 412, 318 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(150) = -1, a(n) > 0 for 0<=n<=149. a(9999988) = 119999861 is the largest value in the first 1+10^7 terms of the sequence. - Gheorghe Coserea, May 24 2016 REFERENCES J. A. Csirik, The genus of X_0(N) is not 150, preprint, 2000. LINKS Gheorghe Coserea, Table of n, a(n) for n = 0..200010 János A. Csirik, Joseph L. Wetherell, Michael E. Zieve, On the genera of X_0(N), arXiv:math/0006096 [math.NT], 2000. FORMULA A001617(a(A001617(n))) = A001617(n) and a(A054729(n)) = -1 for all n>=1. - Gheorghe Coserea, May 22 2016 MATHEMATICA a1617[n_] := 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]; seq[n_] := Module[{inv, bnd}, inv = Table[-1, {n+1}]; bnd = 12n + 18 Floor[Sqrt[n]] + 100; For[k = 1, k <= bnd, k++, g = a1617[k]; If[g <= n && inv[[g+1]] == -1, inv[[g+1]] = k]]; inv]; seq[51] (* Jean-François Alcover, Nov 20 2018, after Gheorghe Coserea and Michael Somos in A001617 *) PROG (PARI) A000089(n) = {   if (n%4 == 0 || n%4 == 3, return(0));   if (n%2 == 0, n \= 2);   my(f = factor(n), fsz = matsize(f)[1]);   prod(k = 1, fsz, if (f[k, 1] % 4 == 3, 0, 2)); }; A000086(n) = {   if (n%9 == 0 || n%3 == 2, return(0));   if (n%3 == 0, n \= 3);   my(f = factor(n), fsz = matsize(f)[1]);   prod(k = 1, fsz, if (f[k, 1] % 3 == 2, 0, 2)); }; A001615(n) = {   my(f = factor(n), fsz = matsize(f)[1],      g = prod(k=1, fsz, (f[k, 1]+1)),      h = prod(k=1, fsz, f[k, 1]));   return((n*g)\h); }; A001616(n) = {   my(f = factor(n), fsz = matsize(f)[1]);   prod(k = 1, fsz, f[k, 1]^(f[k, 2]\2) + f[k, 1]^((f[k, 2]-1)\2)); }; A001617(n) = 1 + A001615(n)/12 - A000089(n)/4 - A000086(n)/3 - A001616(n)/2; seq(n) = {   my(inv = vector(n+1, g, -1), bnd = 12*n + 18*sqrtint(n) + 100, g);   for (k = 1, bnd, g = A001617(k);        if (g <= n && inv[g+1] == -1, inv[g+1] = k));   return(inv); }; seq(51)  \\ Gheorghe Coserea, May 21 2016 CROSSREFS Cf. A001617, A054727, A054729. Sequence in context: A160272 A164006 A178736 * A178897 A013576 A065998 Adjacent sequences:  A054725 A054726 A054727 * A054729 A054730 A054731 KEYWORD sign AUTHOR Janos A. Csirik, Apr 21 2000 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.

Last modified June 2 10:57 EDT 2020. Contains 334771 sequences. (Running on oeis4.)