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A326258
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MM-numbers of unsortable multiset partitions (with empty parts allowed).
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16
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145, 169, 215, 290, 338, 355, 377, 395, 430, 435, 473, 481, 505, 507, 535, 559, 565, 580, 645, 667, 676, 695, 710, 725, 754, 790, 793, 803, 815, 841, 845, 860, 865, 869, 870, 905, 923, 946, 962, 965, 989, 995, 1010, 1014, 1015, 1027, 1065, 1070, 1073, 1075
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OFFSET
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1,1
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The multiset multisystem with MM-number n is obtained by taking the multiset of prime indices of each prime index of n.
A multiset partition is unsortable if no permutation has an ordered concatenation. For example, the multiset partition ((1,2),(1,1,1),(2,2,2)) is sortable because the permutation ((1,1,1),(1,2),(2,2,2)) has concatenation (1,1,1,1,2,2,2,2), which is weakly increasing.
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LINKS
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EXAMPLE
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The sequence of terms together with their multiset multisystems begins:
145: {{2},{1,3}}
169: {{1,2},{1,2}}
215: {{2},{1,4}}
290: {{},{2},{1,3}}
338: {{},{1,2},{1,2}}
355: {{2},{1,1,3}}
377: {{1,2},{1,3}}
395: {{2},{1,5}}
430: {{},{2},{1,4}}
435: {{1},{2},{1,3}}
473: {{3},{1,4}}
481: {{1,2},{1,1,2}}
505: {{2},{1,6}}
507: {{1},{1,2},{1,2}}
535: {{2},{1,1,4}}
559: {{1,2},{1,4}}
565: {{2},{1,2,3}}
580: {{},{},{2},{1,3}}
645: {{1},{2},{1,4}}
667: {{2,2},{1,3}}
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MATHEMATICA
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lexsort[f_, c_]:=OrderedQ[PadRight[{f, c}]];
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], !OrderedQ[Join@@Sort[primeMS/@primeMS[#], lexsort]]&]
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CROSSREFS
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Unsortable set partitions are A058681.
Normal unsortable multiset partitions are A326211.
MM-numbers of crossing multiset partitions are A324170.
MM-numbers of nesting multiset partitions are A326256.
MM-numbers of capturing multiset partitions are A326255.
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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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