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A335125
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Number of anti-run permutations of a multiset whose multiplicities are the prime indices of n.
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8
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1, 1, 0, 2, 0, 1, 0, 6, 2, 0, 0, 6, 0, 0, 1, 24, 0, 12, 0, 2, 0, 0, 0, 36, 2, 0, 30, 0, 0, 10, 0, 120, 0, 0, 1, 84, 0, 0, 0, 24, 0, 3, 0, 0, 38, 0, 0, 240, 2, 18, 0, 0, 0, 246, 0, 6, 0, 0, 0, 96, 0, 0, 24, 720, 0, 0, 0, 0, 0, 14, 0, 660, 0, 0, 74, 0, 1, 0, 0
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OFFSET
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1,4
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COMMENTS
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A multiset whose multiplicities are the prime indices of n (such as row n of A305936) is not the same as the multiset of prime indices of n. For example, the prime indices of 12 are {1,1,2}, while a multiset whose multiplicities are {1,1,2} is {1,1,2,3}.
An anti-run is a sequence with no adjacent equal parts.
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LINKS
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EXAMPLE
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The a(n) permutations for n = 2, 4, 42, 8, 30, 18:
(1) (12) (1212131) (123) (121213) (12123)
(21) (1213121) (132) (121231) (12132)
(1312121) (213) (121312) (12312)
(231) (121321) (12321)
(312) (123121) (13212)
(321) (131212) (21213)
(132121) (21231)
(212131) (21312)
(213121) (21321)
(312121) (23121)
(31212)
(32121)
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MATHEMATICA
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nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]]]];
Table[Length[Select[Permutations[nrmptn[n]], !MatchQ[#, {___, x_, x_, ___}]&]], {n, 100}]
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CROSSREFS
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The version for the prime indices themselves is A335452.
Separable partitions are ranked by A335433.
Separable factorizations are A335434.
Inseparable partitions are ranked by A335448.
Patterns contiguously matched by compositions are A335457.
Strict permutations of prime indices are A335489.
Cf. A019472, A056239, A106351, A112798, A114938, A278990, A292884, A325535, A335407, A335463, A335516, A335838.
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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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