login
A305731
Number of irreducible integer partitions of n.
4
1, 0, 0, 0, 1, 0, 4, 0, 6, 3, 12, 0, 21, 1, 30, 19, 43, 10, 82, 20, 103, 68, 152, 58, 236, 102, 301, 196, 413, 205, 653, 310, 788, 580, 1115, 718, 1649, 1006, 2149, 1714, 3018, 2247, 4502, 3389, 6036, 5509, 8647, 7601, 12678, 11310, 17541
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 22 2018
STATUS
approved