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A335126
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A multiset whose multiplicities are the prime indices of n is inseparable.
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23
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3, 5, 7, 10, 11, 13, 14, 17, 19, 21, 22, 23, 26, 28, 29, 31, 33, 34, 37, 38, 39, 41, 43, 44, 46, 47, 51, 52, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 71, 73, 74, 76, 78, 79, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 101, 102, 103, 104, 106
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OFFSET
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1,1
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COMMENTS
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A multiset is separable if it has a permutation that is an anti-run, meaning there are no adjacent equal parts.
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}.
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LINKS
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EXAMPLE
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The sequence of terms together with the corresponding multisets begins:
3: {1,1}
5: {1,1,1}
7: {1,1,1,1}
10: {1,1,1,2}
11: {1,1,1,1,1}
13: {1,1,1,1,1,1}
14: {1,1,1,1,2}
17: {1,1,1,1,1,1,1}
19: {1,1,1,1,1,1,1,1}
21: {1,1,1,1,2,2}
22: {1,1,1,1,1,2}
23: {1,1,1,1,1,1,1,1,1}
26: {1,1,1,1,1,1,2}
28: {1,1,1,1,2,3}
29: {1,1,1,1,1,1,1,1,1,1}
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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}]]]]];
Select[Range[100], Select[Permutations[nrmptn[#]], !MatchQ[#, {___, x_, x_, ___}]&]=={}&]
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CROSSREFS
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Inseparable partitions are A325535.
Separable factorizations are A335434.
Inseparable factorizations are A333487.
Separable partitions are ranked by A335433.
Inseparable partitions are ranked by A335448.
Anti-run permutations of prime indices are A335452.
Patterns contiguously matched by compositions are A335457.
Cf. A025487, A056239, A106351, A112798, A114938, A181819, A181821, A278990, A292884, A335407, A335489, 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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