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A358910
Number of integer partitions of n whose parts do not have weakly decreasing numbers of prime factors (A001222).
4
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 4, 8, 11, 19, 25, 41, 56, 84, 113, 164, 218, 306, 401, 547, 711, 949, 1218, 1599, 2034, 2625, 3310, 4224, 5283, 6664, 8271, 10336, 12747, 15791, 19343, 23791, 28979, 35398, 42887, 52073, 62779, 75804, 90967, 109291, 130605
OFFSET
0,12
EXAMPLE
The a(9) = 1 through a(14) = 11 partitions:
(54) (541) (74) (543) (76) (554)
(542) (741) (544) (743)
(5411) (5421) (742) (761)
(54111) (5422) (5432)
(5431) (5441)
(7411) (7421)
(54211) (54221)
(541111) (54311)
(74111)
(542111)
(5411111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !GreaterEqual@@PrimeOmega/@#&]], {n, 0, 30}]
CROSSREFS
For sequences of partitions see A141199, compositions A218482.
The case of equality is A319169, for compositions A358911.
The complement is counted by A358909.
A001222 counts prime factors, distinct A001221.
A063834 counts twice-partitions.
Sequence in context: A271723 A212545 A357878 * A212546 A212547 A212548
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 09 2022
STATUS
approved