A305731 Number of irreducible integer partitions of n.

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.

Links

Table of n, a(n) for n=0..50.

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

Cf. A100953, A181819, A182850, A182857, A275870, A304818, A305563, A305733, A305735.

Sequence in context: A127447 A226775 A338682 * A279433 A096272 A340949

Adjacent sequences: A305728 A305729 A305730 * A305732 A305733 A305734

Keyword

nonn

Author

Gus Wiseman, Jun 22 2018

Status

approved