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 A330107 #5 Dec 03 2019 21:13:00
%S A330107 1,3,7,9,13,15,19,21,27,37,39,45,49,53,57,63,69,81,89,91,105,111,113,
%T A330107 117,131,133,135,141,147,151,159,161,165,169,171,183,189,195,207,223,
%U A330107 225,243,247,259,267,273,281,285,309,311,315,329,333,339,343,351,359
%N A330107 MM-numbers of brute-force normalized multiset partitions.
%C A330107 A multiset partition is a finite multiset of finite nonempty multisets of positive integers.
%C A330107 We define the brute-force 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 least representative, where the ordering of multisets is first by length and then lexicographically.
%C A330107 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 A330107 Brute-force: 43287: {{1},{2,3},{2,2,4}}
%C A330107 Lexicographic: 43143: {{1},{2,4},{2,2,3}}
%C A330107 VDD: 15515: {{2},{1,3},{1,1,4}}
%C A330107 MM: 15265: {{2},{1,4},{1,1,3}}
%C A330107 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}}.
%e A330107 The sequence of all brute-force normalized multiset partitions together with their MM-numbers begins:
%e A330107 1: 0 63: {1}{1}{11} 159: {1}{1111}
%e A330107 3: {1} 69: {1}{22} 161: {11}{22}
%e A330107 7: {11} 81: {1}{1}{1}{1} 165: {1}{2}{3}
%e A330107 9: {1}{1} 89: {1112} 169: {12}{12}
%e A330107 13: {12} 91: {11}{12} 171: {1}{1}{111}
%e A330107 15: {1}{2} 105: {1}{2}{11} 183: {1}{122}
%e A330107 19: {111} 111: {1}{112} 189: {1}{1}{1}{11}
%e A330107 21: {1}{11} 113: {123} 195: {1}{2}{12}
%e A330107 27: {1}{1}{1} 117: {1}{1}{12} 207: {1}{1}{22}
%e A330107 37: {112} 131: {11111} 223: {11112}
%e A330107 39: {1}{12} 133: {11}{111} 225: {1}{1}{2}{2}
%e A330107 45: {1}{1}{2} 135: {1}{1}{1}{2} 243: {1}{1}{1}{1}{1}
%e A330107 49: {11}{11} 141: {1}{23} 247: {12}{111}
%e A330107 53: {1111} 147: {1}{11}{11} 259: {11}{112}
%e A330107 57: {1}{111} 151: {1122} 267: {1}{1112}
%t A330107 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A330107 brute[m_]:=If[Union@@m!={}&&Union@@m!=Range[Max@@Flatten[m]],brute[m/.Rule@@@Table[{(Union@@m)[[i]],i},{i,Length[Union@@m]}]],First[Sort[brute[m,1]]]];
%t A330107 brute[m_,1]:=Table[Sort[Sort/@(m/.Rule@@@Table[{i,p[[i]]},{i,Length[p]}])],{p,Permutations[Union@@m]}];
%t A330107 Select[Range[1,100,2],Sort[primeMS/@primeMS[#]]==brute[primeMS/@primeMS[#]]&]
%Y A330107 Equals the odd terms of A330104.
%Y A330107 Non-isomorphic multiset partitions are A007716.
%Y A330107 Cf. A000612, A055621, A283877, A300300, A316983, A317533, A320664, A330061, A330098, A330101, A330103, A330105.
%Y A330107 Other fixed points:
%Y A330107 - Brute-force: A330104 (multisets of multisets), A330107 (multiset partitions), A330099 (set-systems).
%Y A330107 - Lexicographic: A330120 (multisets of multisets), A330121 (multiset partitions), A330110 (set-systems).
%Y A330107 - VDD: A330060 (multisets of multisets), A330097 (multiset partitions), A330100 (set-systems).
%Y A330107 - MM: A330108 (multisets of multisets), A330122 (multiset partitions), A330123 (set-systems).
%Y A330107 - BII: A330109 (set-systems).
%K A330107 nonn,eigen
%O A330107 1,2
%A A330107 _Gus Wiseman_, Dec 02 2019