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A159685
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Maximal number of times a permutation of length n, with prime cycle lengths, can operate on itself before returning to the initial permutation.
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0
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1, 2, 3, 3, 6, 6, 10, 15, 15, 30, 30, 42, 42, 70, 105, 105, 210, 210, 210, 210, 330, 330, 462, 462, 770, 1155, 1155, 2310, 2310, 2730, 2730, 2730, 2730, 4290, 4290, 6006, 6006, 10010, 15015, 15015, 30030, 30030, 30030, 30030, 39270, 39270, 46410, 46410
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Equivalently, largest value of the LCM of the partitions of n into primes.
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EXAMPLE
| A permutation of length 10 can have prime cycle lengths of 2+3+5; so when repeatedly applied to itself, can produce at most 2*3*5 different permutations.
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MATHEMATICA
| temp=Series[Times @@ (1/(1-q[ # ] x^#)& /@ Prepend[Prime /@ Range[24], 1]), {x, 0, Prime[24]}]; Table[Max[List @@ Expand[Coefficient[temp, x^n]]/. q[a_]^_ ->q[a] /.q->Identity], {n, 64}]
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CROSSREFS
| Cf. A077011, A000793, A034891.
Sequence in context: A101437 A039856 A143715 * A187262 A117670 A181695
Adjacent sequences: A159682 A159683 A159684 * A159686 A159687 A159688
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KEYWORD
| nonn
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), Apr 19 2009, May 02 2009
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