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 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.
EXAMPLE
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}}
MATHEMATICA
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]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 22 2019
STATUS
approved