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A001616
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Number of parabolic vertices of GAMMA_0 (n).
(Formerly M0247 N0087)
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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).
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
| 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
| a(n) = sum(d divides n, phi(gcd(d,n/d)) ) where phi() is Euler's totient function. [Joerg Arndt, Jul 17 2011]
Multiplicative with a(p^e) = p^[e/2] + p^[(e-1)/2]. - David W. Wilson, Sep 01, 2001
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MAPLE
| 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
| Table[ Plus@@Map[ EulerPhi[ GCD[ #1, n/#1 ] ]&, Select[ Range[ n ], (Mod[ n, #1 ]==0)& ] ], {n, 1, 100} ]
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PROG
| (PARI) a(n)=sumdiv(n, d, eulerphi(gcd(d, n/d))); /* Joerg Arndt, Jul 17 2011 */
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CROSSREFS
| Sequence in context: A144372 A182861 A049238 * A144371 A101296 A181819
Adjacent sequences: A001613 A001614 A001615 * A001617 A001618 A001619
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KEYWORD
| nonn,easy,nice,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms and Mathematica program Aug 15 1997 (Olivier Gerard).
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