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 A330104 #7 Dec 03 2019 07:09:16
%S A330104 1,2,3,4,6,7,8,9,12,13,14,15,16,18,19,21,24,26,27,28,30,32,36,37,38,
%T A330104 39,42,45,48,49,52,53,54,56,57,60,63,64,69,72,74,76,78,81,84,89,90,91,
%U A330104 96,98,104,105,106,108,111,112,113,114,117,120,126,128,131,133
%N A330104 MM-numbers of brute-force normalized multisets of multisets.
%C A330104 First differs from A330060 and A330108 in having 69 and lacking 35, with corresponding multisets of multisets 69: {{1},{2,2}} and 35: {{2},{1,1}}.
%C A330104 First differs from A330120 in having 435 and lacking 429, with corresponding multisets of multisets 435: {{1},{2},{1,3}} and 429: {{1},{3},{1,2}}.
%C A330104 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 A330104 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 A330104 Brute-force: 43287: {{1},{2,3},{2,2,4}}
%C A330104 Lexicographic: 43143: {{1},{2,4},{2,2,3}}
%C A330104 VDD: 15515: {{2},{1,3},{1,1,4}}
%C A330104 MM: 15265: {{2},{1,4},{1,1,3}}
%C A330104 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 A330104 The sequence of all brute-force normalized multisets of multisets together with their MM-numbers begins:
%e A330104 1: 0 21: {1}{11} 52: {}{}{12} 89: {1112}
%e A330104 2: {} 24: {}{}{}{1} 53: {1111} 90: {}{1}{1}{2}
%e A330104 3: {1} 26: {}{12} 54: {}{1}{1}{1} 91: {11}{12}
%e A330104 4: {}{} 27: {1}{1}{1} 56: {}{}{}{11} 96: {}{}{}{}{}{1}
%e A330104 6: {}{1} 28: {}{}{11} 57: {1}{111} 98: {}{11}{11}
%e A330104 7: {11} 30: {}{1}{2} 60: {}{}{1}{2} 104: {}{}{}{12}
%e A330104 8: {}{}{} 32: {}{}{}{}{} 63: {1}{1}{11} 105: {1}{2}{11}
%e A330104 9: {1}{1} 36: {}{}{1}{1} 64: {}{}{}{}{}{} 106: {}{1111}
%e A330104 12: {}{}{1} 37: {112} 69: {1}{22} 108: {}{}{1}{1}{1}
%e A330104 13: {12} 38: {}{111} 72: {}{}{}{1}{1} 111: {1}{112}
%e A330104 14: {}{11} 39: {1}{12} 74: {}{112} 112: {}{}{}{}{11}
%e A330104 15: {1}{2} 42: {}{1}{11} 76: {}{}{111} 113: {123}
%e A330104 16: {}{}{}{} 45: {1}{1}{2} 78: {}{1}{12} 114: {}{1}{111}
%e A330104 18: {}{1}{1} 48: {}{}{}{}{1} 81: {1}{1}{1}{1} 117: {1}{1}{12}
%e A330104 19: {111} 49: {11}{11} 84: {}{}{1}{11} 120: {}{}{}{1}{2}
%t A330104 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A330104 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 A330104 brute[m_,1]:=Table[Sort[Sort/@(m/.Rule@@@Table[{i,p[[i]]},{i,Length[p]}])],{p,Permutations[Union@@m]}];
%t A330104 Select[Range[100],Sort[primeMS/@primeMS[#]]==brute[primeMS/@primeMS[#]]&]
%Y A330104 Equals the image/fixed points of the idempotent sequence A330105.
%Y A330104 Non-isomorphic multiset partitions are A007716.
%Y A330104 Cf. A000612, A055621, A283877, A316983, A317533, A330098, A330101, A330103.
%Y A330104 Other fixed points:
%Y A330104 - Brute-force: A330104 (multisets of multisets), A330107 (multiset partitions), A330099 (set-systems).
%Y A330104 - Lexicographic: A330120 (multisets of multisets), A330121 (multiset partitions), A330110 (set-systems).
%Y A330104 - VDD: A330060 (multisets of multisets), A330097 (multiset partitions), A330100 (set-systems).
%Y A330104 - MM: A330108 (multisets of multisets), A330122 (multiset partitions), A330123 (set-systems).
%Y A330104 - BII: A330109 (set-systems).
%K A330104 nonn,eigen
%O A330104 1,2
%A A330104 _Gus Wiseman_, Dec 02 2019