

A001766


Index of (the image of) the modular group Gamma(n) in PSL_2(Z).
(Formerly M4098 N1700)


3



1, 6, 12, 24, 60, 72, 168, 192, 324, 360, 660, 576, 1092, 1008, 1440, 1536, 2448, 1944, 3420, 2880, 4032, 3960, 6072, 4608, 7500, 6552, 8748, 8064, 12180, 8640, 14880, 12288, 15840, 14688, 20160, 15552, 25308, 20520, 26208, 23040, 34440, 24192, 39732, 31680
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OFFSET

1,2


COMMENTS

Equivalently, the degree of the modular curve X(N) as a cover of the jline.


REFERENCES

R. C. Gunning, Lectures on Modular Forms. Princeton Univ. Press, Princeton, NJ, 1962, p. 15.
B. Schoeneberg, Elliptic Modular Functions, SpringerVerlag, NY, 1974, p. 76.
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 = 1..1000
Ioannis Ivrissimtzis, David Singerman, James Strudwick, From Farey fractions to the Klein quartic and beyond, arXiv:1909.08568 [math.GR], 2019. See mu(n) p. 3.
Index entries for sequences related to modular groups


FORMULA

a(n) = n * A000114(n).  Michael Somos, Jan 29 2004
a(n) = ((n^3)/2)*Product_{p  n, p prime} (11/p^2), for n>=3.  Michel Marcus, Oct 23 2019


MAPLE

proc(n) local b, d: b := (n^3)/2: for d from 1 to n do if irem(n, d) = 0 and isprime(d) then b := b*(1d^(2)): fi: od: RETURN(b): end:


MATHEMATICA

Table[ (n^3)/If[ n>2, 2, 1 ] Times@@(11/Select[ Range[ n ], (Mod[ n, #1 ]==0&&PrimeQ[ #1 ])& ]^2), {n, 1, 45} ] (* Olivier Gérard, Aug 15 1997 *)


PROG

(PARI) a(n) = if (n==1, 1, if (n==2, 6, my(f=factor(n)); prod(k=1, #f~, 11/f[k, 1]^2)*n^3/2)); \\ Michel Marcus, Oct 23 2019


CROSSREFS

Equals A000056(n) for n = 2 and (1/2)*A000056(n) for n > 2 (since I is contained in Gamma(2) but not in Gamma(n) for n > 2).
Sequence in context: A091629 A089529 A300915 * A110959 A303398 A244743
Adjacent sequences: A001763 A001764 A001765 * A001767 A001768 A001769


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Olivier Gérard, Aug 15 1997
Definition corrected by Mira Bernstein, May 30 2006


STATUS

approved



