Search: id:A000113
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%I A000113
%S A000113 1,3,4,3,6,12,8,6,4,18,12,12,14,24,24,6,18,12,20,18,32,36,
%T A000113 24,24,30,42,12,24,30,72,32,12,48,54,48,12,38,60,56,36,42,
%U A000113 96,44,36,24,72,48,24,56,90,72,42,54,36,72,48,80,90,60,72
%N A000113 Number of transformation groups of order n.
%D A000113 B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, 
               p. 139.
%H A000113 T. D. Noe, <a href="b000113.txt">Table of n, a(n) for n = 1..10000</a>
%F A000113 Let psi(m) = A001615(m) (Dedekind's psi function). Write n = 2^i*3^j*k, 
               where (6,k) = 1 and let i' = floor(i/2) for i < 6, i' = 3 for i >
               = 6; let j' = 0 for j = 0 or 1, j' = 1 for j >= 2. Then a(n) = psi(n/
               (2^i'*3^j')) = psi(n)/(2^i'*3^j').
%F A000113 Multiplicative with a(2^e)=3*2^Floor[(e-1)/2] for 0<e<7, a(2^e)=3*2^(e-4) 
               for e>=7, a(3^e)=4 for 0<e<3, a(3^e)=4*3^(e-2) for e>=3 and a(p^e)=(p+1)*p^(e-1) 
               for p>3. - T. D. Noe (noe(AT)sspectra.com), Nov 14 2006
%Y A000113 Sequence in context: A073181 A046897 A109506 this_sequence A069915 A033634 
               A111970
%Y A000113 Adjacent sequences: A000110 A000111 A000112 this_sequence A000114 A000115 
               A000116
%K A000113 nonn,easy,mult
%O A000113 1,2
%A A000113 N. J. A. Sloane (njas(AT)research.att.com).

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