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%I A002809 M0577 N0210 #47 Oct 29 2023 13:07:23
%S A002809 1,2,3,4,6,12,15,20,30,60,84,105,140,210,420,840,1260,1540,2310,2520,
%T A002809 4620,5460,9240,13860,16380,27720,30030,32760,60060,120120,180180,
%U A002809 360360,471240,510510,556920,1021020,1141140,2042040,3063060,3423420,6126120,6846840
%N A002809 Increasing values of A000793 (largest order of permutation of n elements).
%D A002809 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002809 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002809 Giovanni Resta, <a href="/A002809/b002809.txt">Table of n, a(n) for n = 1..10000</a> (first 3318 terms from Alois P. Heinz)
%H A002809 Marc Deléglise and Jean-Louis Nicolas, <a href="http://arxiv.org/abs/1207.0603">Maximal product of primes whose sum is bounded</a>, arXiv preprint arXiv:1207.0603 [math.NT], 2012. - From _N. J. A. Sloane_, Dec 17 2012
%H A002809 J.-L. Nicolas, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa14/aa14120.pdf">Sur l'ordre maximum d'un élément dans le groupe S_n des permutations</a>, Acta Arith., 14 (1968), 315-332.
%H A002809 J.-L. Nicolas, <a href="http://archive.numdam.org/article/BSMF_1969__97__129_0.pdf">Ordre maximal d'un élément du groupe S_n de permutations et 'highly composite numbers'</a>, Bull. Math. Soc. France 97 (1969) 129-191.
%t A002809 b[n_, i_] := b[n, i] = Module[{p}, p = If[i<1, 1, Prime[i]]; If[n == 0 || i<1, 1, Max[b[n, i-1], Table[p^j*b[n-p^j, i-1], {j, 1, Log[p, n] // Floor}]]]]; a[n_] := b[n, If[n<8, 3, PrimePi[Ceiling[1.328*Sqrt[n*Log[n] // Floor]]]]]; Table[a[n], {n, 0, 100}] // Union (* _Jean-François Alcover_, Mar 07 2014, after _Alois P. Heinz_ *)
%Y A002809 Indices are A006644.
%Y A002809 Cf. A000793.
%K A002809 nonn,nice
%O A002809 1,2
%A A002809 _N. J. A. Sloane_
%E A002809 Description improved Apr 15 1997. More terms from _David W. Wilson_.

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