OFFSET
0,7
COMMENTS
A multiset m whose distinct elements are m_1, m_2, ..., m_k with multiplicities y_1, y_2, ..., y_k is irreducible if m is of size > 1 and either gcd(m_1, ..., m_k) > 1 or the multiset {y_1, ..., y_k} is irreducible.
EXAMPLE
The a(6) = 4 irreducible partitions are (42), (33), (222), (2211).
MATHEMATICA
ptnredQ[y_]:=Or[Length[y]==1, And[GCD@@y==1, ptnredQ[Sort[Length/@Split[y], Greater]]]];
Table[Length[Select[IntegerPartitions[n], !ptnredQ[#]&]], {n, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 22 2018
STATUS
approved