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A054728 a(n) = 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

FORMULA

A001617(a(A001617(n))) = A001617(n) and a(A054729(n)) = -1 for all n>=1. - Gheorghe Coserea, May 22 2016

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

nonn

AUTHOR

Janos A. Csirik, Apr 21 2000

STATUS

approved

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Last modified February 23 23:06 EST 2018. Contains 299595 sequences. (Running on oeis4.)