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Number of positive integers less than n with more prime factors than n, counted with multiplicity.
6

%I #8 Jan 02 2019 21:47:05

%S 0,0,0,0,1,0,2,0,1,1,5,0,6,2,2,0,9,1,10,1,5,5,13,0,6,6,2,2,18,2,19,0,

%T 10,10,10,1,24,11,11,1,27,5,28,5,5,15,31,0,16,6,17,6,36,2,19,2,20,20,

%U 41,2,42,21,9,0,23,10,47,10,25,10,50,1,51,27,11,11

%N Number of positive integers less than n with more prime factors than n, counted with multiplicity.

%e Column n lists the a(n) positive integers less than n with more prime factors than n:

%e 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

%e ---------------------------------------------------------------------

%e 4 6 8 8 10 12 12 12 16 16 18 16

%e 4 9 10 8 8 15 16

%e 8 9 14 15

%e 6 8 12 14

%e 4 6 10 12

%e 4 9 10

%e 8 9

%e 6 8

%e 4 6

%e 4

%t Table[Length[Select[Range[n],PrimeOmega[#]>PrimeOmega[n]&]],{n,100}]

%Y Positions of zeros appear to be A029744.

%Y Cf. A000010, A000961, A001221, A001222, A045920, A058933, A061142, A067003, A302242, A322839, A322841.

%K nonn

%O 1,7

%A _Gus Wiseman_, Dec 28 2018