Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Jun 03 2018 02:07:07
%S 144,162,174,186,192,198,200,204,216,220,222,228,230,234,238,240,246,
%T 250,252,258,260,264,266,270,276,280,282,288,290,294,300,306,308,310,
%U 312,318,320,322,324,330,336,340,342,348,350,354,360,364,366,370,372,374
%N Numbers n such that 2 * A243823(n) > n.
%C Consider A243823(n), which is the number of m < n that are products of at least one prime p | n and at least one prime q that does not divide n. These numbers m in the cototient of n do not divide a power of n. This sequence lists numbers n where such numbers m are predominant.
%H Michael De Vlieger, <a href="/A294575/b294575.txt">Table of n, a(n) for n = 1..10000</a>
%e A272619(10) = (6), A243823(10) = 1, so 10 is not in the sequence. A243823(144) = 74, which is greater than half of all numbers less than or equal to 144, thus 144 is the first term.
%t Select[Range[10^3], Function[n, 2 (n - (Count[Range@ n, _?(PowerMod[n, Floor@ Log2@ n, #] == 0 &)] + EulerPhi[n] - 1)) > n]]
%Y Cf. A243823, A272619, A294576.
%K nonn
%O 1,1
%A _Michael De Vlieger_, Nov 17 2017