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Number of totally aperiodic integer partitions of n.
1

%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