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 A330121 #5 Dec 06 2019 09:36:23
%S A330121 1,3,7,9,13,15,19,21,27,37,39,45,49,53,57,63,69,81,89,91,105,111,113,
%T A330121 117,131,133,135,141,147,151,159,161,165,169,171,183,189,195,207,223,
%U A330121 225,243,247,259,267,273,281,285,309,311,315,329,333,339,343,351,359
%N A330121 MM-numbers of lexicographically normalized multiset partitions.
%C A330121 First differs from A330107 in lacking 435 and having 429, with corresponding multisets of multisets 435: {{1},{2},{1,3}} and 429: {{1},{3},{1,2}}.
%C A330121 We define the lexicographic 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 lexicographically least of these representatives.
%C A330121 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 A330121 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 A330121 Brute-force: 43287: {{1},{2,3},{2,2,4}}
%C A330121 Lexicographic: 43143: {{1},{2,4},{2,2,3}}
%C A330121 VDD: 15515: {{2},{1,3},{1,1,4}}
%C A330121 MM: 15265: {{2},{1,4},{1,1,3}}
%e A330121 The sequence of all lexicographically normalized multiset partitions together with their MM-numbers begins:
%e A330121 1: 63: {1}{1}{11} 159: {1}{1111}
%e A330121 3: {1} 69: {1}{22} 161: {11}{22}
%e A330121 7: {11} 81: {1}{1}{1}{1} 165: {1}{2}{3}
%e A330121 9: {1}{1} 89: {1112} 169: {12}{12}
%e A330121 13: {12} 91: {11}{12} 171: {1}{1}{111}
%e A330121 15: {1}{2} 105: {1}{2}{11} 183: {1}{122}
%e A330121 19: {111} 111: {1}{112} 189: {1}{1}{1}{11}
%e A330121 21: {1}{11} 113: {123} 195: {1}{2}{12}
%e A330121 27: {1}{1}{1} 117: {1}{1}{12} 207: {1}{1}{22}
%e A330121 37: {112} 131: {11111} 223: {11112}
%e A330121 39: {1}{12} 133: {11}{111} 225: {1}{1}{2}{2}
%e A330121 45: {1}{1}{2} 135: {1}{1}{1}{2} 243: {1}{1}{1}{1}{1}
%e A330121 49: {11}{11} 141: {1}{23} 247: {12}{111}
%e A330121 53: {1111} 147: {1}{11}{11} 259: {11}{112}
%e A330121 57: {1}{111} 151: {1122} 267: {1}{1112}
%Y A330121 Equals the odd terms of A330120.
%Y A330121 A subset of A320634.
%Y A330121 MM-weight is A302242.
%Y A330121 Non-isomorphic multiset partitions are A007716.
%Y A330121 Cf. A056239, A112798, A317533, A320456, A330061, A330098, A330103, A330105, A330194.
%Y A330121 Other fixed points:
%Y A330121 - Brute-force: A330104 (multisets of multisets), A330107 (multiset partitions), A330099 (set-systems).
%Y A330121 - Lexicographic: A330120 (multisets of multisets), A330121 (multiset partitions), A330110 (set-systems).
%Y A330121 - VDD: A330060 (multisets of multisets), A330097 (multiset partitions), A330100 (set-systems).
%Y A330121 - MM: A330108 (multisets of multisets), A330122 (multiset partitions), A330123 (set-systems).
%Y A330121 - BII: A330109 (set-systems).
%K A330121 nonn
%O A330121 1,2
%A A330121 _Gus Wiseman_, Dec 05 2019