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%I #4 Jan 09 2020 18:13:45
%S 1,1,2,2,2,2,3,3,4,4,4,5,5,6,6,7,7,8,8,9,10,10,11,12,13,14,15,16,17,
%T 18,19,20,21,23,24,25,27,28,30,32,34,35,37,39,41,44,46,48,51,53,56,59,
%U 61,64,68,71,74,78,81,85,89,93,97,101,106,111,115,120,126
%N Nearest integer to P(n)/Q(n) = A000041(n)/A000009(n).
%C Conjecture: This sequence is nondecreasing. More generally, the rational sequence A000041(n)/A000009(n) is nondecreasing for n > 5.
%t Table[Round[PartitionsP[n]/PartitionsQ[n]],{n,0,100}]
%Y The numerators are A330994.
%Y The denominators are A330995.
%Y The same for factorizations is A331048.
%Y Cf. A000009, A000041, A001055, A003238, A035359, A045778, A046063, A331022.
%K nonn
%O 0,3
%A _Gus Wiseman_, Jan 08 2020