This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A305731 #9 Jun 23 2018 14:20:49
%S A305731 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,
%T A305731 102,301,196,413,205,653,310,788,580,1115,718,1649,1006,2149,1714,
%U A305731 3018,2247,4502,3389,6036,5509,8647,7601,12678,11310,17541
%N A305731 Number of irreducible integer partitions of n.
%C A305731 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.
%e A305731 The a(6) = 4 irreducible partitions are (42), (33), (222), (2211).
%t A305731 ptnredQ[y_]:=Or[Length[y]==1,And[GCD@@y==1,ptnredQ[Sort[Length/@Split[y],Greater]]]];
%t A305731 Table[Length[Select[IntegerPartitions[n],!ptnredQ[#]&]],{n,20}]
%Y A305731 Cf. A100953, A181819, A182850, A182857, A275870, A304818, A305563, A305733, A305735.
%K A305731 nonn
%O A305731 0,7
%A A305731 _Gus Wiseman_, Jun 22 2018