A211168 Exponent of alternating group An.
1, 1, 3, 6, 30, 60, 420, 420, 1260, 2520, 27720, 27720, 360360, 360360, 360360, 360360, 6126120, 12252240, 232792560, 232792560, 232792560, 232792560, 5354228880, 5354228880, 26771144400, 26771144400, 80313433200, 80313433200, 2329089562800, 2329089562800
Offset: 1
Examples
For n = 7, lcm{1,...,5,7} = 420.
Links
- Alexander Gruber, Table of n, a(n) for n = 1..2308
Crossrefs
Programs
-
Magma
for n in [1..40] do Exponent(AlternatingGroup(n)); end for;
-
Magma
for n in [1..40] do if n mod 2 eq 0 then L := [1..n-1]; else L := Append([1..n-2],n); end if; LCM(L); end for;
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Mathematica
Table[If[Mod[n, 2] == 0, LCM @@ Range[n - 1], LCM @@ Join[Range[n - 2], {n}]], {n, 1, 100}] (* or *) a[1] = 1; a[2] = 1; a[3] = 3; a[n_] := a[n] = If[Mod[n, 2] == 0, LCM[a[n - 1], n - 2], LCM[a[n - 2], n - 3, n]]; Table[a[n], {n, 1, 40}]
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PARI
a(n)=lcm(if(n%2,concat([2..n-2],n),[2..n-1])) \\ Charles R Greathouse IV, Mar 02 2014
Formula
Explicit:
a(n) = lcm{1, ..., n-1} if n is even.
= lcm{1, ..., n-2, n} if n is odd.
Recursive:
Let a(1) = a(2) = 1 and a(3) = 3. Then
a(n) = lcm{a(n-1), n-2} if n is even.
= lcm{a(n-2), n-3, n} if n is odd.
Comments