Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Sep 29 2018 01:50:07
%S 1,1,2,3,6,7,14,17,27,34,55,63,99,117,162,203,286,333,469,558,737,903,
%T 1196,1414,1860,2232,2839,3422,4359,5144,6531,7762,9617,11479,14182,
%U 16715,20630,24333,29569,34890,42335,49515,59871,70042,83810,98105,117152
%N Number of totally aperiodic integer partitions of n.
%C An integer partition is totally aperiodic iff either it is strict or it is aperiodic with totally aperiodic multiplicities.
%e The a(6) = 7 aperiodic integer partitions are: (6), (51), (42), (411), (321), (3111), (21111). The first aperiodic integer partition that is not totally aperiodic is (432211).
%t totaperQ[m_]:=Or[UnsameQ@@m,And[GCD@@Length/@Split[Sort[m]]==1,totaperQ[Sort[Length/@Split[Sort[m]]]]]];
%t Table[Length[Select[IntegerPartitions[n],totaperQ]],{n,30}]
%Y Cf. A000837, A018783, A047966, A098859, A100953, A305563, A319149, A319160, A319162, A319163, A319164, A319810.
%K nonn
%O 1,3
%A _Gus Wiseman_, Sep 28 2018