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A318809
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Number of necklace permutations of the multiset of prime indices of n > 1.
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1
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1
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OFFSET
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1,30
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COMMENTS
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A necklace is a finite sequence that is minimal among its cyclic permutations.
a(1) = 1 by convention.
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LINKS
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EXAMPLE
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The a(144) = 3 necklace permutations of {1,1,1,1,2,2} are: (111122), (111212), (112112).
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And];
Table[Length[Select[Permutations[primeMS[n]], neckQ]], {n, 2, 200}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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