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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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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).
Sequence in context: A082505 A091629 A089529 this_sequence A110959 A065106 A030775
Adjacent sequences: A001763 A001764 A001765 this_sequence A001767 A001768 A001769
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms and Mma program Aug 15 1997 from Olivier Gerard.
Definition corrected by Mira Bernstein, May 30 2006
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