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A326333 Number of integer partitions of n with sortable prime factors. 2
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 76, 99, 132, 171, 222, 283, 363, 457, 577, 721, 902, 1115, 1379, 1693, 2076, 2530, 3077, 3723, 4500, 5410, 6494, 7765, 9270, 11025, 13089, 15491, 18307, 21569, 25369, 29765, 34869, 40750, 47546, 55361, 64367, 74685, 86529 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

An integer partition has sortable prime factors if there is a permutation (c_1,...,c_k) of the parts such that the maximum prime factor of c_i is at most the minimum prime factor of c_{i+1}. For example, the partition (27,8,6) is sortable because the permutation (8,6,27) satisfies the condition.

LINKS

Table of n, a(n) for n=0..48.

FORMULA

A000041(n) = a(n) + A326332(n).

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], OrderedQ[Join@@Sort[First/@FactorInteger[#]&/@#, OrderedQ[PadRight[{#1, #2}]]&]]&]], {n, 0, 20}]

CROSSREFS

Unsortable integer partitions are A326332.

Sortable normal multiset partitions are A326212.

Sortable factorizations are A326334.

Cf. A000041, A000108, A001055, A058681, A112798, A326209, A326211, A326258.

Sequence in context: A008640 A008634 A238869 * A036011 A325856 A104501

Adjacent sequences:  A326330 A326331 A326332 * A326334 A326335 A326336

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 27 2019

STATUS

approved

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Last modified May 18 22:57 EDT 2021. Contains 344007 sequences. (Running on oeis4.)