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A298941 Number of permutations of the multiset of prime factors of n > 1 that are Lyndon words. 6
1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 0, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 3, 1, 1, 1, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,29

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..20000

EXAMPLE

The a(90) = 3 Lyndon permutations are {2,3,3,5}, {2,3,5,3}, {2,5,3,3}.

MAPLE

with(combinat): with(numtheory):

g:= l-> (n-> `if`(n=0, 1, add(mobius(j)*multinomial(n/j,

        (l/j)[]), j=divisors(igcd(l[])))/n))(add(i, i=l)):

a:= n-> g(map(i-> i[2], ifactors(n)[2])):

seq(a(n), n=2..150);  # Alois P. Heinz, Feb 09 2018

MATHEMATICA

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

LyndonQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And]&&Array[RotateRight[q, #]&, Length[q], 1, UnsameQ];

Table[Length[Select[Permutations[primeMS[n]], LyndonQ]], {n, 2, 60}]

CROSSREFS

Cf. A000740, A001037, A001222, A008480, A008965, A059966, A060223, A096443, A112798, A215366, A275024, A294859, A298947.

Sequence in context: A203947 A081396 A194293 * A317146 A194297 A100544

Adjacent sequences:  A298938 A298939 A298940 * A298942 A298943 A298944

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 29 2018

STATUS

approved

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Last modified March 30 16:16 EDT 2020. Contains 333127 sequences. (Running on oeis4.)