%I A136185
%S A136185 1,2,3,5,7,11,14,20,25,33,40,51,60,74,86,103,118,139,157,182,204,233,
%T A136185 259,293,323,362,397,441,481,531,576,632,683,745,802,871,934,1010,1080,
%U A136185 1163,1240,1331,1415,1514,1606,1713,1813,1929,2037,2162,2279,2413,2539
%N A136185 Number of metacyclic groups of order p^n, prime p >= 3.
%C A136185 For number of metacyclic groups of order 2^n see A136184.
%H A136185 Klaus Brockhaus, <a href="b136185.txt">Table of n, a(n) for n=1..1000</
               a> [Values computed with MAGMA]
%H A136185 MAGMA Computational Algebra System, V2.14-1, <a href="http://magma.maths.usyd.edu.au/
               magma/htmlhelp/text701.htm#6850">Metacyclic p-groups</a>
%F A136185 G.f. (conjectured): -x*(x^7 - 2*x^5 + x^3 + x^2 - x - 1)/((x - 1)^4*(x 
               + 1)^2*(x^2 + x + 1)).
%e A136185 a(4) = 5 since there are five metacyclic groups of order p^4; they have 
               invariants <4, 0, 0, 4, [ p^4 ], >, <1, 2, 1, 2, [], >, <1, 2, 2, 
               2, [], >, <2, 2, 2, 2, [], > and <1, 3, 1, 1, [], > resp. (for details 
               see MAGMA link).
%o A136185 (MAGMA) [ NumberOfMetacyclicPGroups(3, n): n in [1..53] ];
%Y A136185 Cf. A136184.
%Y A136185 Sequence in context: A029982 A070026 A036608 this_sequence A026812 A001402 
               A008629
%Y A136185 Adjacent sequences: A136182 A136183 A136184 this_sequence A136186 A136187 
               A136188
%K A136185 nonn
%O A136185 1,2
%A A136185 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 19 2007