This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A330108 #5 Dec 05 2019 17:41:28
%S A330108 1,2,3,4,6,7,8,9,12,13,14,15,16,18,19,21,24,26,27,28,30,32,35,36,37,
%T A330108 38,39,42,45,48,49,52,53,54,56,57,60,63,64,70,72,74,76,78,81,84,89,90,
%U A330108 91,95,96,98,104,105,106,108,111,112,113,114,117,120,126,128
%N A330108 MM-numbers of MM-normalized multisets of multisets.
%C A330108 First differs from A330060 in having 175 and lacking 207, with corresponding multisets of multisets 175: {{2},{2},{1,1}} and 207: {{1},{1},{2,2}}.
%C A330108 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 of multisets with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset of multisets with MM-number 78 is {{},{1},{1,2}}.
%C A330108 We define the MM-normalization of a multiset of multisets to be obtained by first normalizing so that the vertices cover an initial interval of positive integers, then applying all permutations to the vertex set, and finally taking the representative with the smallest MM-number.
%C A330108 For example, 15301 is the MM-number of {{3},{1,2},{1,1,4}}, which has the following normalizations together with their MM-numbers:
%C A330108 Brute-force: 43287: {{1},{2,3},{2,2,4}}
%C A330108 Lexicographic: 43143: {{1},{2,4},{2,2,3}}
%C A330108 VDD: 15515: {{2},{1,3},{1,1,4}}
%C A330108 MM: 15265: {{2},{1,4},{1,1,3}}
%e A330108 The sequence of all MM-normalized multisets of multisets together with their MM-numbers begins:
%e A330108 1: 0 21: {1}{11} 49: {11}{11} 84: {}{}{1}{11}
%e A330108 2: {} 24: {}{}{}{1} 52: {}{}{12} 89: {1112}
%e A330108 3: {1} 26: {}{12} 53: {1111} 90: {}{1}{1}{2}
%e A330108 4: {}{} 27: {1}{1}{1} 54: {}{1}{1}{1} 91: {11}{12}
%e A330108 6: {}{1} 28: {}{}{11} 56: {}{}{}{11} 95: {2}{111}
%e A330108 7: {11} 30: {}{1}{2} 57: {1}{111} 96: {}{}{}{}{}{1}
%e A330108 8: {}{}{} 32: {}{}{}{}{} 60: {}{}{1}{2} 98: {}{11}{11}
%e A330108 9: {1}{1} 35: {2}{11} 63: {1}{1}{11} 104: {}{}{}{12}
%e A330108 12: {}{}{1} 36: {}{}{1}{1} 64: {}{}{}{}{}{} 105: {1}{2}{11}
%e A330108 13: {12} 37: {112} 70: {}{2}{11} 106: {}{1111}
%e A330108 14: {}{11} 38: {}{111} 72: {}{}{}{1}{1} 108: {}{}{1}{1}{1}
%e A330108 15: {1}{2} 39: {1}{12} 74: {}{112} 111: {1}{112}
%e A330108 16: {}{}{}{} 42: {}{1}{11} 76: {}{}{111} 112: {}{}{}{}{11}
%e A330108 18: {}{1}{1} 45: {1}{1}{2} 78: {}{1}{12} 113: {123}
%e A330108 19: {111} 48: {}{}{}{}{1} 81: {1}{1}{1}{1} 114: {}{1}{111}
%t A330108 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A330108 mmnorm[m_]:=If[Union@@m!={}&&Union@@m!=Range[Max@@Flatten[m]],mmnorm[m/.Rule@@@Table[{(Union@@m)[[i]],i},{i,Length[Union@@m]}]],First[SortBy[brute[m,1],Map[Times@@Prime/@#&,#,{0,1}]&]]];
%t A330108 brute[m_,1]:=Table[Sort[Sort/@(m/.Rule@@@Table[{i,p[[i]]},{i,Length[p]}])],{p,Permutations[Union@@m]}];
%t A330108 Select[Range[100],Sort[primeMS/@primeMS[#]]==mmnorm[primeMS/@primeMS[#]]&]
%Y A330108 Equals the image/fixed points of the idempotent sequence A330194.
%Y A330108 A subset of A320456.
%Y A330108 Non-isomorphic multiset partitions are A007716.
%Y A330108 MM-weight is A302242.
%Y A330108 Cf. A056239, A112798, A317533, A330061, A330098, A330103, A330105.
%Y A330108 Other fixed points:
%Y A330108 - Brute-force: A330104 (multisets of multisets), A330107 (multiset partitions), A330099 (set-systems).
%Y A330108 - Lexicographic: A330120 (multisets of multisets), A330121 (multiset partitions), A330110 (set-systems).
%Y A330108 - VDD: A330060 (multisets of multisets), A330097 (multiset partitions), A330100 (set-systems).
%Y A330108 - MM: A330108 (multisets of multisets), A330122 (multiset partitions), A330123 (set-systems).
%Y A330108 - BII: A330109 (set-systems).
%K A330108 nonn,eigen
%O A330108 1,2
%A A330108 _Gus Wiseman_, Dec 05 2019