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A061350
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Maximal size of Aut(G) where G is a finite Abelian group of order n.
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3
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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; internal format)
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OFFSET
| 1,3
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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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1024
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MAPLE
| 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:
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CROSSREFS
| Cf. A059773, A002884, A053290, A053292, A053293.
Sequence in context: A021795 A008904 A074382 * A046276 A003571 A068457
Adjacent sequences: A061347 A061348 A061349 * A061351 A061352 A061353
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KEYWORD
| nonn,mult,nice,easy
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AUTHOR
| Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 07 2001
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 12 2001
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