A317246 Heinz numbers of supernormal integer partitions.

1, 2, 4, 6, 8, 12, 16, 18, 30, 32, 60, 64, 90, 128, 150, 180, 210, 256, 300, 360, 450, 512, 540, 600, 1024, 1350, 1500, 2048, 2250, 2310, 2520, 3780, 4096, 4200, 5880, 8192, 9450, 10500, 12600, 13230, 15750, 16384, 17640, 18900, 20580, 26460, 29400, 30030

Offset

1,2

Comments

An integer partition is supernormal if either (1) it is of the form 1^n for some n >= 0, or (2a) it spans an initial interval of positive integers, and (2b) its multiplicities, sorted in weakly decreasing order, are themselves a supernormal integer partition.

Links

Table of n, a(n) for n=1..48.

Index entries for sequences related to Heinz numbers

Example

Sequence of supernormal integer partitions begins: (), (1), (11), (21), (111), (211), (1111), (221), (321), (11111), (3211), (111111), (3221), (1111111), (3321), (32211), (4321).

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
supnrm[q_]:=Or[q=={}||Union[q]=={1}, And[Union[q]==Range[Max[q]], supnrm[Sort[Length/@Split[q], Greater]]]];
Select[Range[10000], supnrm[primeMS[#]]&]

Crossrefs

Cf. A055932, A056239, A181819, A182850, A296150, A304465, A304687, A304818, A305732, A305733, A317089, A317090, A317245.

Sequence in context: A007694 A322492 A332276 * A279686 A219653 A050622

Adjacent sequences: A317243 A317244 A317245 * A317247 A317248 A317249

Keyword

nonn

Author

Gus Wiseman, Jul 24 2018

Status

approved