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 A321270 #5 Nov 02 2018 11:23:31
%S A321270 1,1,2,1,3,2,5,1,5,4,7,3,11,7,10,1,15,9,22,7,19,12,30,5,22,19,28,14,
%T A321270 42,22,56,1,33,30,42,20,77,45
%N A321270 Number of connected multiset partitions of a multiset whose multiplicities are the prime indices of n.
%C A321270 This multiset (row n of A305936) is generally not the same as the multiset of prime indices of n. For example, the prime indices of 12 are {1,1,2}, while a multiset whose multiplicities are {1,1,2} is {1,1,2,3}.
%e A321270 The a(2) = 1 through a(12) = 3 connected multiset partitions:
%e A321270 {{1}} {{11}} {{12}} {{111}} {{112}} {{1111}}
%e A321270 {{1}{1}} {{1}{11}} {{1}{12}} {{1}{111}}
%e A321270 {{1}{1}{1}} {{11}{11}}
%e A321270 {{1}{1}{11}}
%e A321270 {{1}{1}{1}{1}}
%e A321270 .
%e A321270 {{123}} {{1122}} {{1112}} {{11111}} {{1123}}
%e A321270 {{1}{122}} {{1}{112}} {{1}{1111}} {{1}{123}}
%e A321270 {{12}{12}} {{11}{12}} {{11}{111}} {{12}{13}}
%e A321270 {{2}{112}} {{1}{1}{12}} {{1}{1}{111}}
%e A321270 {{1}{2}{12}} {{1}{11}{11}}
%e A321270 {{1}{1}{1}{11}}
%e A321270 {{1}{1}{1}{1}{1}}
%e A321270 The a(18) = 9, a(27) = 28, and a(36) = 20 connected multiset partitions of {1,1,2,2,3}, {1,1,2,2,3,3}, and {1,1,2,2,3,4} respectively:
%e A321270 {{1,1,2,2,3}} {{1,1,2,2,3,3}} {{1,1,2,2,3,4}}
%e A321270 {{1},{1,2,2,3}} {{1},{1,2,2,3,3}} {{1},{1,2,2,3,4}}
%e A321270 {{1,2},{1,2,3}} {{1,1,2},{2,3,3}} {{1,1,2},{2,3,4}}
%e A321270 {{1,3},{1,2,2}} {{1,1,3},{2,2,3}} {{1,2},{1,2,3,4}}
%e A321270 {{2},{1,1,2,3}} {{1,2},{1,2,3,3}} {{1,2,2},{1,3,4}}
%e A321270 {{2,3},{1,1,2}} {{1,2,2},{1,3,3}} {{1,2,3},{1,2,4}}
%e A321270 {{1},{1,2},{2,3}} {{1,2,3},{1,2,3}} {{1,3},{1,2,2,4}}
%e A321270 {{1},{2},{1,2,3}} {{1,3},{1,2,2,3}} {{1,4},{1,2,2,3}}
%e A321270 {{2},{1,2},{1,3}} {{2},{1,1,2,3,3}} {{2},{1,1,2,3,4}}
%e A321270 {{2,3},{1,1,2,3}} {{2,3},{1,1,2,4}}
%e A321270 {{3},{1,1,2,2,3}} {{2,4},{1,1,2,3}}
%e A321270 {{1},{1,2},{2,3,3}} {{1},{1,2},{2,3,4}}
%e A321270 {{1},{1,3},{2,2,3}} {{1},{2},{1,2,3,4}}
%e A321270 {{1},{2},{1,2,3,3}} {{1,2},{1,3},{2,4}}
%e A321270 {{1,2},{1,3},{2,3}} {{1,2},{1,4},{2,3}}
%e A321270 {{1},{2,3},{1,2,3}} {{1},{2,3},{1,2,4}}
%e A321270 {{1},{3},{1,2,2,3}} {{1},{2,4},{1,2,3}}
%e A321270 {{2},{1,2},{1,3,3}} {{2},{1,2},{1,3,4}}
%e A321270 {{2},{1,3},{1,2,3}} {{2},{1,3},{1,2,4}}
%e A321270 {{2},{2,3},{1,1,3}} {{2},{1,4},{1,2,3}}
%e A321270 {{2},{3},{1,1,2,3}}
%e A321270 {{3},{1,2},{1,2,3}}
%e A321270 {{3},{1,3},{1,2,2}}
%e A321270 {{3},{2,3},{1,1,2}}
%e A321270 {{1},{2},{1,3},{2,3}}
%e A321270 {{1},{2},{3},{1,2,3}}
%e A321270 {{1},{3},{1,2},{2,3}}
%e A321270 {{2},{3},{1,2},{1,3}}
%Y A321270 Cf. A007718, A007719, A056156, A181821, A191970, A300913, A305193, A305936, A318284, A318286, A319557, A321272.
%K A321270 nonn,more
%O A321270 1,3
%A A321270 _Gus Wiseman_, Nov 01 2018