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Search: id:A001616
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| A001616 |
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Number of parabolic vertices of GAMMA_0 (n).
(Formerly M0247 N0087)
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+0
10
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| 1, 2, 2, 3, 2, 4, 2, 4, 4, 4, 2, 6, 2, 4, 4, 6, 2, 8, 2, 6, 4, 4, 2, 8, 6, 4, 6, 6, 2, 8, 2, 8, 4, 4, 4, 12, 2, 4, 4, 8, 2, 8, 2, 6, 8, 4, 2, 12, 8, 12, 4, 6, 2, 12, 4, 8, 4, 4, 2, 12, 2, 4, 8, 12, 4, 8, 2, 6, 4, 8, 2, 16, 2, 4, 12, 6, 4, 8, 2, 12, 12, 4, 2, 12, 4, 4, 4, 8, 2, 16, 4, 6, 4, 4, 4, 16
(list; graph; listen)
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OFFSET
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1,2
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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).
Fell, Harriet; Newman, Morris; Ordman, Edward; Tables of genera of groups of linear fractional transformations. J. Res. Nat. Bur. Standards Sect. B 67B 1963 61-68.
B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, p. 102.
G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton, 1971, see p. 25, Eq. (4).
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..1000
S. R. Finch, Modular forms on SL_2(Z)
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FORMULA
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Multiplicative with a(p^e) = p^[e/2] + p^[(e-1)/2]. - David W. Wilson, Sep 01, 2001
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MAPLE
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with(numtheory); nupara := proc (n) local b, d; b := 0; for d to n do if modp(n, d) = 0 then b := b+eval(phi(gcd(d, n/d))) fi od; b end: (Gene Smith, May 22 2006)
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MATHEMATICA
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Table[ Plus@@Map[ EulerPhi[ GCD[ #1, n/#1 ] ]&, Select[ Range[ n ], (Mod[ n, #1 ]==0)& ] ], {n, 1, 100} ]
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CROSSREFS
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Adjacent sequences: A001613 A001614 A001615 this_sequence A001617 A001618 A001619
Sequence in context: A134681 A144372 A049238 this_sequence A144371 A101296 A077462
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KEYWORD
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nonn,easy,nice,mult
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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 (Olivier Gerard).
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