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A051593 Largest order of even permutation of n elements, or maximal order of element of alternating group A_n. 8
1, 1, 1, 3, 3, 5, 5, 7, 15, 15, 21, 21, 35, 35, 60, 105, 105, 105, 140, 210, 210, 420, 420, 420, 420, 840, 1155, 1260, 1365, 1540, 2310, 2520, 4620, 4620, 5460, 5460, 9240, 9240, 13860, 15015, 16380, 16380, 27720, 30030, 32760, 60060, 60060, 60060 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
REFERENCES
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985.
V. Jovovic, Some combinatorial characteristics of symmetric and alternating groups (in Russian), Belgrade, 1980, unpublished.
LINKS
FORMULA
a(n)=max{ A000793(n-2), A051704(n-1), A051704(n) }, a(0)=a(1)=1.
MATHEMATICA
(* a3 = A000793 a4 = A051704 *) a3[n_] := Max[LCM @@@ IntegerPartitions[n]]; a4[n_] := (pp = Reap[ Do[ pk = p^k; If[pk <= n, Sow[pk]], {p, Prime[ Range[2, PrimePi[n]]]}, {k, 1, Ceiling[ Log[3, n]]}]][[2, 1]]; sel = Select[ IntegerPartitions[n, All, pp], Length[#] == Length[ Union[#] && !MatchQ[#, {___, x_, ___, y_, ___} /; GCD[x, y] != 1]] &]; Max[Times @@@ sel]); a4[0] = 1; a4[1] = a4[2] = a4[4] = a4[6] = 0; a[n_] := Max[a3[n - 2], a4[n - 1], a4[n]]; a[0] = a[1] = a[2] = 1; Table[a[n], {n, 0, 47}] (* Jean-François Alcover, Sep 11 2012, from formula *)
PROG
(PARI) a(n)={my(m=1); forpart(p=n, if(sum(i=1, #p, p[i]-1)%2==0, m=max(m, lcm(Vec(p))))); m} \\ Andrew Howroyd, Jul 03 2018
CROSSREFS
Sequence in context: A142456 A098508 A355572 * A142712 A247577 A282207
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved

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Last modified February 23 14:24 EST 2024. Contains 370283 sequences. (Running on oeis4.)