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Search: id:A001766
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| A001766 |
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Index of (the image of) the modular group Gamma(n) in PSL_2(Z).
(Formerly M4098 N1700)
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Equivalently, the degree of the modular curve X(N) as a cover of the j-line.
a(n)=n*A000114(n). - Michael Somos Jan 29 2004
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
R. C. Gunning, Lectures on Modular Forms. Princeton Univ. Press, Princeton, NJ, 1962, p. 15.
B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, p. 76.
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LINKS
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Index entries for sequences related to modular groups
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MAPLE
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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*(1-d^(-2)): fi: od: RETURN(b): end:
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MATHEMATICA
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Table[ (n^3)/If[ n>2, 2, 1 ] Times@@(1-1/Select[ Range[ n ], (Mod[ n, #1 ]==0&&PrimeQ[ #1 ])& ]^2), {n, 1, 45} ]
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CROSSREFS
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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).
Adjacent sequences: A001763 A001764 A001765 this_sequence A001767 A001768 A001769
Sequence in context: A082505 A091629 A089529 this_sequence A110959 A065106 A030775
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms and Mathematica program Aug 15 1997 from Olivier Gerard.
Definition corrected by Mira Bernstein, May 30 2006
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