A321472 Heinz numbers of integer partitions whose parts can be further partitioned and flattened to obtain the partition (k, ..., 3, 2, 1) for some k.

2, 5, 6, 13, 21, 22, 25, 29, 30, 46, 47, 57, 73, 85, 86, 91, 102, 107, 121, 123, 130, 142, 147, 151, 154, 165, 175, 185, 197, 201, 206, 210, 217, 222, 257, 298, 299

Offset: 1

Author

Gus Wiseman, Nov 13 2018

Keywords

• nonn

Comments

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

These partitions are those that are coarser than (k, ..., 3, 2, 1) in the poset of integer partitions of 1 + 2 + ... + k, for some k, ordered by refinement.

Examples

			The sequence of all integer partitions whose Heinz numbers are in the sequence begins: (1), (3), (2,1), (6), (4,2), (5,1), (3,3), (10), (3,2,1), (9,1), (15), (8,2), (21), (7,3), (14,1), (6,4), (7,2,1), (28), (5,5), (13,2), (6,3,1), (20,1), (4,4,2), (36), (5,4,1), (5,3,2), (4,3,3), (12,3), (45), (19,2), (27,1), (4,3,2,1).
		

Crossrefs

Subsequence of A242422.

Cf. A001970, A002846, A056239, A066723, A112798, A213427, A242422, A265947, A300383, A317141.

Cf. A321467, A321468, A321470, A321471, A321514.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[2,200],Select[Sort/@Join@@@Tuples[IntegerPartitions/@primeMS[#]],Sort[#]==Range[Max@@#]&]!={}&]