The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A061350 Maximal size of Aut(G) where G is a finite Abelian group of order n. 4
 1, 1, 2, 6, 4, 2, 6, 168, 48, 4, 10, 12, 12, 6, 8, 20160, 16, 48, 18, 24, 12, 10, 22, 336, 480, 12, 11232, 36, 28, 8, 30, 9999360, 20, 16, 24, 288, 36, 18, 24, 672, 40, 12, 42, 60, 192, 22, 46, 40320, 2016, 480, 32, 72, 52, 11232, 40, 1008, 36, 28, 58, 48, 60, 30, 288 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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). Equivalently, maximal size of Aut(G) where G is a nilpotent group of order n. - Eric M. Schmidt, Feb 27 2013 LINKS T. D. Noe, Table of n, a(n) for n=1..1024 MAPLE A061350 := proc(n) local ans, i, j; ans := 1: for i from 1 to nops(ifactors(n)) do ans := ans*(mul(ifactors(n)[i]^ifactors(n)[i] - ifactors(n)[i]^(j - 1), j = 1..ifactors(n)[i])): od: RETURN(ans) end: MATHEMATICA a[p_?PrimeQ] := p-1; a = 1; a[n_] := Times @@ (Product[#[]^#[] - #[]^k, {k, 0, #[]-1}]& /@ FactorInteger[n]); Table[a[n], {n, 1, 63}] (* Jean-François Alcover, May 21 2012, after Maple *) CROSSREFS Cf. A059773, A002884, A053290, A053292, A053293. Sequence in context: A021795 A008904 A074382 * A046276 A283614 A333520 Adjacent sequences:  A061347 A061348 A061349 * A061351 A061352 A061353 KEYWORD nonn,mult,nice,easy AUTHOR Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 07 2001 EXTENSIONS More terms from Vladeta Jovovic, Jun 12 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 30 18:07 EDT 2020. Contains 334728 sequences. (Running on oeis4.)