%I #7 Jul 30 2018 22:16:15

%S 9,24,25,27,36,40,48,49,54,56,72,80,81,88,96,100,104,108,112,120,121,

%T 125,135,136,144,152,160,162,168,169,176,184,189,192,196,200,208,216,

%U 224,225,232,240,243,248,250,264,270,272,280,288,289,296,297,304,312

%N Heinz numbers of integer partitions that are not fully normal.

%C An integer partition is fully normal if either it is of the form (1,1,...,1) or its multiplicities span an initial interval of positive integers and, sorted in weakly decreasing order, are themselves fully normal.

%e Sequence of all integer partitions that are not fully normal begins: (22), (2111), (33), (222), (2211), (3111), (21111), (44), (2221), (4111), (22111), (31111), (2222), (5111), (211111), (3311).

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t fulnrmQ[ptn_]:=With[{qtn=Sort[Length/@Split[ptn],Greater]},Or[ptn=={}||Union[ptn]=={1},And[Union[qtn]==Range[Max[qtn]],fulnrmQ[qtn]]]];

%t Select[Range[100],!fulnrmQ[Reverse[primeMS[#]]]&]

%Y Cf. A055932, A056239, A181819, A182850, A296150, A305733, A317089, A317090, A317245, A317246, A317491, A317492.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jul 30 2018