Search: id:A128604
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%I A128604
%S A128604 1,1,2,1,1,5,2,1,1,14,1,1,1,2,5,1,1,51,1,1,1,1,2,1,1,1,267,1,1,1,1,15,
               1,
%T A128604 1,1,1,1,1,1,1,2,5,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,67,
               1,
%U A128604 1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,5,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A128604 Number of groups of order A128603(n).
%C A128604 Number of groups whose order divides p^6 for p a prime.
%C A128604 The groups of these orders (up to A128603(54403784) = 1073741789 in version 
               V2.13-4) form a class contained in the Small Groups Library of MAGMA. 
               (corrected Mar 18 2007)
%H A128604 Klaus Brockhaus, <a href="b128604.txt">Table of n, a(n) for n=1..10000</
               a>
%H A128604 MAGMA Documentation, <a href="http://magma.maths.usyd.edu.au/magma/htmlhelp/
               text404.htm">Database of Small Groups</a>
%F A128604 a(n) = A000001(A128603(n)).
%e A128604 A128603(10) = 16 and there are 14 groups of order 16 (A000001(16) = 14), 
               hence a(10) = 14.
%o A128604 (MAGMA) D:=SmallGroupDatabase(); [ NumberOfSmallGroups(D, n) : n in [ 
               k: k in [1..455] | exists(t) {x: x in [t: t in [1..6] ] | IsPower(k, 
               x) and IsPrime(Iroot(k, x)) } ] ];
%Y A128604 Cf. A000001 (number of groups of order n), A128603 (numbers dividing 
               p^6 for p a prime), A098885 (number of groups of prime power orders).
%Y A128604 Sequence in context: A022661 A120292 A162470 this_sequence A098885 A106270 
               A047888
%Y A128604 Adjacent sequences: A128601 A128602 A128603 this_sequence A128605 A128606 
               A128607
%K A128604 nonn
%O A128604 1,3
%A A128604 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 13 2007

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