A317492 Heinz numbers of fully normal integer partitions.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78

Offset

1,2

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

Table of n, a(n) for n=1..67.

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

Cf. A055932, A056239, A181819, A182850, A296150, A305732, A317089, A317090, A317245, A317246, A317491, A317493.

Sequence in context: A072886 A031980 A183221 * A324721 A327534 A305732

Adjacent sequences: A317489 A317490 A317491 * A317493 A317494 A317495

Keyword

nonn

Author

Gus Wiseman, Jul 30 2018

Status

approved