OFFSET
1,3
COMMENTS
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}.
EXAMPLE
The a(2) = 1 through a(12) = 3 connected multiset partitions:
{{1}} {{11}} {{12}} {{111}} {{112}} {{1111}}
{{1}{1}} {{1}{11}} {{1}{12}} {{1}{111}}
{{1}{1}{1}} {{11}{11}}
{{1}{1}{11}}
{{1}{1}{1}{1}}
.
{{123}} {{1122}} {{1112}} {{11111}} {{1123}}
{{1}{122}} {{1}{112}} {{1}{1111}} {{1}{123}}
{{12}{12}} {{11}{12}} {{11}{111}} {{12}{13}}
{{2}{112}} {{1}{1}{12}} {{1}{1}{111}}
{{1}{2}{12}} {{1}{11}{11}}
{{1}{1}{1}{11}}
{{1}{1}{1}{1}{1}}
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:
{{1,1,2,2,3}} {{1,1,2,2,3,3}} {{1,1,2,2,3,4}}
{{1},{1,2,2,3}} {{1},{1,2,2,3,3}} {{1},{1,2,2,3,4}}
{{1,2},{1,2,3}} {{1,1,2},{2,3,3}} {{1,1,2},{2,3,4}}
{{1,3},{1,2,2}} {{1,1,3},{2,2,3}} {{1,2},{1,2,3,4}}
{{2},{1,1,2,3}} {{1,2},{1,2,3,3}} {{1,2,2},{1,3,4}}
{{2,3},{1,1,2}} {{1,2,2},{1,3,3}} {{1,2,3},{1,2,4}}
{{1},{1,2},{2,3}} {{1,2,3},{1,2,3}} {{1,3},{1,2,2,4}}
{{1},{2},{1,2,3}} {{1,3},{1,2,2,3}} {{1,4},{1,2,2,3}}
{{2},{1,2},{1,3}} {{2},{1,1,2,3,3}} {{2},{1,1,2,3,4}}
{{2,3},{1,1,2,3}} {{2,3},{1,1,2,4}}
{{3},{1,1,2,2,3}} {{2,4},{1,1,2,3}}
{{1},{1,2},{2,3,3}} {{1},{1,2},{2,3,4}}
{{1},{1,3},{2,2,3}} {{1},{2},{1,2,3,4}}
{{1},{2},{1,2,3,3}} {{1,2},{1,3},{2,4}}
{{1,2},{1,3},{2,3}} {{1,2},{1,4},{2,3}}
{{1},{2,3},{1,2,3}} {{1},{2,3},{1,2,4}}
{{1},{3},{1,2,2,3}} {{1},{2,4},{1,2,3}}
{{2},{1,2},{1,3,3}} {{2},{1,2},{1,3,4}}
{{2},{1,3},{1,2,3}} {{2},{1,3},{1,2,4}}
{{2},{2,3},{1,1,3}} {{2},{1,4},{1,2,3}}
{{2},{3},{1,1,2,3}}
{{3},{1,2},{1,2,3}}
{{3},{1,3},{1,2,2}}
{{3},{2,3},{1,1,2}}
{{1},{2},{1,3},{2,3}}
{{1},{2},{3},{1,2,3}}
{{1},{3},{1,2},{2,3}}
{{2},{3},{1,2},{1,3}}
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 01 2018
STATUS
approved