OFFSET
2,6
COMMENTS
In Klein and Fricke, the level n is called Stufenzahlen, the congruence group is denoted by Gamma_{n} and the genus is called Geschlecht and denoted by p. - Michael Somos, Nov 08 2014
REFERENCES
R. C. Gunning, Lectures on Modular Forms. Princeton Univ. Press, Princeton, NJ, 1962, p. 15.
B. Iversen, Hyperbolic Geometry, Cambridge Univ. Press, 1992, see p. 238.
F. Klein and R. Fricke, Vorlesungen ueber die theorie der elliptischen modulfunctionen, Teubner, Leipzig, 1890, Vol. 1, see p. 398.
Russian Encyclopedia of Mathematics, Vol. 3, page 931.
B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, p. 94.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 2..1000
Ioannis Ivrissimtzis, David Singerman, James Strudwick, From Farey fractions to the Klein quartic and beyond, arXiv:1909.08568 [math.GR], 2019. See g(n) p. 3.
FORMULA
EXAMPLE
G.f. = x^6 + 3*x^7 + 5*x^8 + 10*x^9 + 13*x^10 + 26*x^11 + 25*x^12 + ...
MATHEMATICA
Join[{0}, Table[1 + n^2 (n - 6)/24 Product[If[Mod[n, Prime[p]] == 0, 1 - 1/Prime[p]^2, 1], {p, PrimePi[n]}], {n, 3, 100}]] (* T. D. Noe, Aug 10 2012 *)
a[ n_] := If[ n < 3, 0, 1 + n^2 (n - 6)/24 Product[ If[ PrimeQ[p] && Divisible[n, p], 1 - 1/p^2, 1], {p, 2, n}]]; (* Michael Somos, Nov 08 2014 *)
PROG
(PARI) {a(n) = if(n<3, 0, 1 + n^2 * (n-6) / 24 * prod(p=2, n, if( isprime(p) && (n%p==0), 1 - 1/p^2, 1)))}; /* Michael Somos, May 19 2004 */
(PARI)
a(n) = {
if (n < 6, 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 + (n-6)*sqr(n\g)*h\24);
};
vector(52, n, a(n+1)) \\ Gheorghe Coserea, Oct 23 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved