%I A001616 M0247 N0087
%S A001616 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,
%T A001616 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,
%U A001616 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
%N A001616 Number of parabolic vertices of GAMMA_0 (n).
%D A001616 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.
%D A001616 B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, 
               p. 102.
%D A001616 G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, 
               Princeton, 1971, see p. 25, Eq. (4).
%D A001616 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001616 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001616 N. J. A. Sloane, <a href="b001616.txt">Table of n, a(n) for n = 1..1000</
               a>
%H A001616 S. R. Finch, <A HREF="http://algo.inria.fr/bsolve/">Modular forms on 
               SL_2(Z)</A>
%F A001616 Multiplicative with a(p^e) = p^[e/2] + p^[(e-1)/2]. - David W. Wilson, 
               Sep 01, 2001
%p A001616 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)
%t A001616 Table[ Plus@@Map[ EulerPhi[ GCD[ #1, n/#1 ] ]&, Select[ Range[ n ], (Mod[ 
               n, #1 ]==0)& ] ], {n, 1, 100} ]
%Y A001616 Sequence in context: A134681 A144372 A049238 this_sequence A144371 A101296 
               A077462
%Y A001616 Adjacent sequences: A001613 A001614 A001615 this_sequence A001617 A001618 
               A001619
%K A001616 nonn,easy,nice,mult
%O A001616 1,2
%A A001616 N. J. A. Sloane (njas(AT)research.att.com).
%E A001616 More terms and Mathematica program Aug 15 1997 (Olivier Gerard).