OFFSET
1,2
COMMENTS
A multiset is aperiodic if its multiplicities are relatively prime. For this sequence neither the parts nor their multiset union are required to be aperiodic, only the multiset of parts.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..50
FORMULA
a(n) = Sum_{d|n} mu(d) * A007716(n/d).
EXAMPLE
Non-isomorphic representatives of the a(3) = 9 aperiodic multiset partitions are:
{{1,1,1}}, {{1,2,2}}, {{1,2,3}},
{{1},{1,1}}, {{1},{2,2}}, {{1},{2,3}}, {{2},{1,2}},
{{1},{2},{2}}, {{1},{2},{3}}.
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 26 2018
STATUS
approved