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A326257
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MM-numbers of weakly nesting multiset partitions.
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11
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49, 91, 98, 133, 147, 169, 182, 196, 203, 245, 247, 259, 266, 273, 294, 299, 301, 338, 343, 361, 364, 371, 377, 392, 399, 406, 427, 441, 455, 481, 490, 494, 497, 507, 518, 529, 532, 539, 546, 551, 553, 559, 588, 598, 602, 609, 623, 637, 665, 667, 676, 686, 689
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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 weakly nesting if it has two blocks of the form {...x,y...}, {...z,t...} where x <= z and t <= y or z <= x and y <= t.
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LINKS
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EXAMPLE
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The sequence of terms together with their multiset multisystems begins:
49: {{1,1},{1,1}}
91: {{1,1},{1,2}}
98: {{},{1,1},{1,1}}
133: {{1,1},{1,1,1}}
147: {{1},{1,1},{1,1}}
169: {{1,2},{1,2}}
182: {{},{1,1},{1,2}}
196: {{},{},{1,1},{1,1}}
203: {{1,1},{1,3}}
245: {{2},{1,1},{1,1}}
247: {{1,2},{1,1,1}}
259: {{1,1},{1,1,2}}
266: {{},{1,1},{1,1,1}}
273: {{1},{1,1},{1,2}}
294: {{},{1},{1,1},{1,1}}
299: {{1,2},{2,2}}
301: {{1,1},{1,4}}
338: {{},{1,2},{1,2}}
343: {{1,1},{1,1},{1,1}}
361: {{1,1,1},{1,1,1}}
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MATHEMATICA
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wknXQ[stn_]:=MatchQ[stn, {___, {___, x_, y_, ___}, ___, {___, z_, t_, ___}, ___}/; (x<=z&&y>=t)||(x>=z&&y<=t)]
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], wknXQ[primeMS/@primeMS[#]]&]
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CROSSREFS
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MM-numbers of crossing multiset partitions are A324170.
MM-numbers of nesting multiset partitions are A324256.
MM-numbers of capturing multiset partitions are A326255.
Nesting set partitions are A016098.
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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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