A321472 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..37.

EXAMPLE

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).

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@@#]&]!={}&]

CROSSREFS

Subsequence of A242422.

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

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

Sequence in context: A181314 A027010 A038191 * A087128 A154365 A247959

Adjacent sequences: A321469 A321470 A321471 * A321473 A321474 A321475

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 13 2018

STATUS

approved