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A326257 MM-numbers of weakly nesting multiset partitions. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
LINKS
EXAMPLE
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}}
MATHEMATICA
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[#]]&]
CROSSREFS
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.
Sequence in context: A093894 A259766 A273937 * A231275 A158725 A090825
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 21 2019
STATUS
approved

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Last modified June 15 11:51 EDT 2024. Contains 373407 sequences. (Running on oeis4.)