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A351202
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Number of permutations of the multiset of prime factors of n (or ordered prime factorizations of n) with all distinct runs.
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20
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1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 4, 1, 2, 1, 2, 1, 6, 1, 1, 2, 2, 2, 2, 1, 2, 2, 4, 1, 6, 1, 2, 2, 2, 1, 4, 1, 2, 2, 2, 1, 4, 2, 4, 2, 2, 1, 6, 1, 2, 2, 1, 2, 6, 1, 2, 2, 6, 1, 4, 1, 2, 2, 2, 2, 6, 1, 4, 1, 2, 1, 6, 2, 2, 2
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OFFSET
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1,6
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LINKS
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EXAMPLE
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The a(36) = 2 permutations are (1,1,2,2), (2,2,1,1). Missing are: (1,2,1,2), (1,2,2,1), (2,1,1,2), (2,1,2,1). Here we use prime indices instead of factors.
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MATHEMATICA
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Table[Length[Select[Permutations[Join@@ ConstantArray@@@FactorInteger[n]], UnsameQ@@Split[#]&]], {n, 100}]
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CROSSREFS
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The maximum number of possible permutations is A008480.
A005811 counts runs in binary expansion.
A044813 lists numbers whose binary expansion has distinct run-lengths.
A098859 counts partitions with distinct multiplicities, ordered A242882.
A283353 counts normal multisets with a permutation without distinct runs.
A297770 counts distinct runs in binary expansion.
A351014 counts distinct runs in standard compositions, firsts A351015.
A351204 = partitions whose perms. have distinct runs, complement A351203.
Counting words with all distinct runs:
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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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