OFFSET
1,1
COMMENTS
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.
EXAMPLE
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).
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
fulnrmQ[ptn_]:=With[{qtn=Sort[Length/@Split[ptn], Greater]}, Or[ptn=={}||Union[ptn]=={1}, And[Union[qtn]==Range[Max[qtn]], fulnrmQ[qtn]]]];
Select[Range[100], !fulnrmQ[Reverse[primeMS[#]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 30 2018
STATUS
approved