Search: id:A061350
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%I A061350
%S A061350 1,1,2,6,4,2,6,168,48,4,10,12,12,6,8,20160,16,48,18,24,12,10,22,336,
%T A061350 480,12,11232,36,28,8,30,9999360,20,16,24,288,36,18,24,672,40,12,42,60,
%U A061350 192,22,46,40320,2016,480,32,72,52,11232,40,1008,36,28,58,48,60,30,288
%N A061350 Maximal size of Aut(G) where G is a finite Abelian group of order n.
%C A061350 a(n) is multiplicative; if n = p^m is a prime power the maximal size 
               of Aut(G) is attained by the elementary Abelian group G =(C_p)^m 
               and then Aut(G) is GL(m,p) and a(n) = (p^m - 1)*(p^m - p)*...*(p^m 
               - p^(m-1)). For general n the maximum will be for the direct product 
               of the (C_p)^m over the prime powers dividing n and then the automorphism 
               group is the direct product of the GL(m,p).
%H A061350 T. D. Noe, <a href="b061350.txt">Table of n, a(n) for n=1..1024</a>
%p A061350 A061350 := proc(n) local ans, i, j; ans := 1: for i from 1 to nops(ifactors(n)[2]) 
               do ans := ans*(mul(ifactors(n)[2][i][1]^ifactors(n)[2][i][2] - ifactors(n)[2][i][1]^(j 
               - 1), j = 1..ifactors(n)[2][i][2])): od: RETURN(ans) end:
%Y A061350 Cf. A059773, A002884, A053290, A053292, A053293.
%Y A061350 Sequence in context: A021795 A008904 A074382 this_sequence A046276 A003571 
               A068457
%Y A061350 Adjacent sequences: A061347 A061348 A061349 this_sequence A061351 A061352 
               A061353
%K A061350 nonn,mult,nice,easy
%O A061350 1,3
%A A061350 Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 07 2001
%E A061350 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 12 2001

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