login
A303547
Number of non-isomorphic periodic multiset partitions of weight n.
11
0, 1, 1, 4, 1, 13, 1, 33, 10, 94, 1, 327, 1, 913, 100, 3017, 1, 10233, 1, 34236, 919, 119372, 1, 432234, 91, 1574227, 9945, 5916177, 1, 22734231, 1, 89003059, 119378, 356058543, 1000, 1453509039, 1, 6044132797, 1574233, 25612601420, 1, 110509543144, 1, 485161348076
OFFSET
1,4
COMMENTS
A multiset is periodic if its multiplicities have a common divisor greater than 1. For this sequence neither the parts nor their multiset union are required to be periodic, only the multiset of parts.
FORMULA
a(n) = 1 if n is prime.
a(n) = A007716(n) - A303546(n).
EXAMPLE
Non-isomorphic representatives of the a(4) = 4 multiset partitions are {{1,1},{1,1}}, {{1,2},{1,2}}, {{1},{1},{1},{1}}, {{1},{1},{2},{2}}.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 26 2018
EXTENSIONS
More terms from Jinyuan Wang, Jun 21 2020
STATUS
approved