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A051593 Largest order of even permutation of n elements, or maximal order of element of alternating group A_n. 6
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V. Jovovic, Some combinatorial characteristics of symmetric and alternating groups (in Russian), Belgrade, 1980, unpublished.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-Fran├žois 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: A092316 A142456 A098508 * 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 August 20 10:17 EDT 2019. Contains 326149 sequences. (Running on oeis4.)