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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 V. Jovovic, Some combinatorial characteristics of symmetric and alternating groups (in Russian), Belgrade, 1980, unpublished.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 Table of n, a(n) for n=0..47. Index entries for sequences related to groups 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 Cf. A057742, A057743, A057740, A000793. Sequence in context: A142456 A098508 A355572 * A142712 A247577 A282207 Adjacent sequences: A051590 A051591 A051592 * A051594 A051595 A051596 KEYWORD nonn,nice,easy AUTHOR Vladeta Jovovic STATUS approved

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