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 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. 7
 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 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

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Last modified June 24 14:24 EDT 2021. Contains 345417 sequences. (Running on oeis4.)