This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A358910 #6 Dec 10 2022 10:47:25
%S A358910 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,
%T A358910 547,711,949,1218,1599,2034,2625,3310,4224,5283,6664,8271,10336,12747,
%U A358910 15791,19343,23791,28979,35398,42887,52073,62779,75804,90967,109291,130605
%N A358910 Number of integer partitions of n whose parts do not have weakly decreasing numbers of prime factors (A001222).
%e A358910 The a(9) = 1 through a(14) = 11 partitions:
%e A358910 (54) (541) (74) (543) (76) (554)
%e A358910 (542) (741) (544) (743)
%e A358910 (5411) (5421) (742) (761)
%e A358910 (54111) (5422) (5432)
%e A358910 (5431) (5441)
%e A358910 (7411) (7421)
%e A358910 (54211) (54221)
%e A358910 (541111) (54311)
%e A358910 (74111)
%e A358910 (542111)
%e A358910 (5411111)
%t A358910 Table[Length[Select[IntegerPartitions[n],!GreaterEqual@@PrimeOmega/@#&]],{n,0,30}]
%Y A358910 For sequences of partitions see A141199, compositions A218482.
%Y A358910 The case of equality is A319169, for compositions A358911.
%Y A358910 The complement is counted by A358909.
%Y A358910 A001222 counts prime factors, distinct A001221.
%Y A358910 A063834 counts twice-partitions.
%Y A358910 Cf. A056239, A300335, A320324, A358831, A358902, A358903, A358908.
%K A358910 nonn
%O A358910 0,12
%A A358910 _Gus Wiseman_, Dec 09 2022