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

Author

Gus Wiseman, Jul 24 2018

Keywords

• nonn

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.

Examples

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

Links

• Index entries for sequences related to Heinz numbers

Crossrefs

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

Programs

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[#]]&]