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A322839 Numbers n with more prime factors (counted with multiplicity) than n+1.

%I A322839 #13 Jan 17 2023 06:27:00
%S A322839 4,6,8,10,12,16,18,20,22,24,28,30,32,36,40,42,45,46,48,50,52,54,56,58,
%T A322839 60,64,66,68,70,72,76,78,80,81,82,84,88,90,92,96,100,102,104,105,106,
%U A322839 108,110,112,114,117,120,126,128,130,132,136,138,140,144,148,150
%N A322839 Numbers n with more prime factors (counted with multiplicity) than n+1.
%C A322839 First differs from A074827 in having 104.
%H A322839 Robert Israel, <a href="/A322839/b322839.txt">Table of n, a(n) for n = 1..10000</a>
%e A322839 104 has four prime factors (2, 2, 2, 13), while 105 has only three (3, 5, 7), so 104 belongs to the sequence.
%p A322839 R:= NULL: count:= 0: w:= 0:
%p A322839 for n from 2 while count < 100 do
%p A322839   v:= numtheory:-bigomega(n);
%p A322839   if v < w then R:= R,n-1; count:= count+1; fi;
%p A322839   w:= v;
%p A322839 od:
%p A322839 R; # _Robert Israel_, Jan 16 2023
%t A322839 Select[Range[100],PrimeOmega[#]>PrimeOmega[#+1]&]
%t A322839 Position[Partition[PrimeOmega[Range[200]],2,1],_?(#[[1]]>#[[2]]&),1,Heads -> False]//Flatten (* _Harvey P. Dale_, Jan 02 2021 *)
%Y A322839 Cf. A000961, A001221, A001222, A045920, A294277, A294278, A302242, A322838, A322840.
%K A322839 nonn
%O A322839 1,1
%A A322839 _Gus Wiseman_, Dec 28 2018