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A317493 Heinz numbers of integer partitions that are not fully normal. 3
9, 24, 25, 27, 36, 40, 48, 49, 54, 56, 72, 80, 81, 88, 96, 100, 104, 108, 112, 120, 121, 125, 135, 136, 144, 152, 160, 162, 168, 169, 176, 184, 189, 192, 196, 200, 208, 216, 224, 225, 232, 240, 243, 248, 250, 264, 270, 272, 280, 288, 289, 296, 297, 304, 312 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
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
Sequence in context: A161431 A223379 A223297 * A102217 A124065 A121453
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 30 2018
STATUS
approved

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)