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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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4
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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, 24192, 39732, 31680
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OFFSET
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1,2
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COMMENTS
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Equivalently, the degree of the modular curve X(N) as a cover of the j-line.
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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.
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).
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LINKS
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FORMULA
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a(n) = ((n^3)/2)*Product_{p | n, p prime} (1-1/p^2), for n>=3. - Michel Marcus, Oct 23 2019
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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} ] (* Olivier Gérard, Aug 15 1997 *)
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PROG
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(PARI) a(n) = if (n==1, 1, if (n==2, 6, my(f=factor(n)); prod(k=1, #f~, 1-1/f[k, 1]^2)*n^3/2)); \\ Michel Marcus, Oct 23 2019
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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).
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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