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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 (list; graph; refs; listen; history; text; internal format)
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: A200692 A127447 A226775 * A279433 A096272 A340949

Adjacent sequences:  A305728 A305729 A305730 * A305732 A305733 A305734

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 22 2018

STATUS

approved

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Last modified April 17 11:50 EDT 2021. Contains 343064 sequences. (Running on oeis4.)