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A111905 Numbers k such that more primes, among primes <= the largest prime dividing k, divide k than do not.

%I A111905 #19 Jun 23 2024 04:59:11
%S A111905 2,4,6,8,10,12,15,16,18,20,24,30,32,36,40,42,45,48,50,54,60,64,66,70,
%T A111905 72,75,80,84,90,96,100,105,108,110,120,126,128,132,135,140,144,150,
%U A111905 154,160,162,165,168,180,192,198,200,210,216,220,225,231,240,250,252,256,264
%N A111905 Numbers k such that more primes, among primes <= the largest prime dividing k, divide k than do not.
%H A111905 John Tyler Rascoe, <a href="/A111905/b111905.txt">Table of n, a(n) for n = 1..1000</a>
%e A111905 20 is included because 5 is the largest prime dividing 20. And of the primes <= 5 (2,3,5), 2 and 5 (2 primes) divide 20, 3 (only 1 prime) does not divide 20.
%o A111905 (PARI) {m=270;v=vector(m);for(n=2,m,f=factor(n)[,1]~;c=0;pc=0;forprime(p=2,vecmax(f), j=1;s=length(f);while(j<=s&&p!=f[j],j++);if(j<=s,c++);pc++);v[n]=sign(pc-2*c)); for(n=1,m,if(v[n]<0,print1(n,",")))} \\ _Klaus Brockhaus_, Aug 21 2005
%o A111905 (Python)
%o A111905 from itertools import count, islice
%o A111905 from sympy import sieve, factorint
%o A111905 def a_gen():
%o A111905     for n in count(2):
%o A111905         f = [sieve.search(i)[0] for i in factorint(n)]
%o A111905         if len(f) > f[-1]//2:
%o A111905             yield n
%o A111905 A111905_list = list(islice(a_gen(), 100)) # _John Tyler Rascoe_, Jun 22 2024
%Y A111905 Cf. A111906, A111907.
%K A111905 nonn
%O A111905 1,1
%A A111905 _Leroy Quet_, Aug 19 2005
%E A111905 More terms from _Klaus Brockhaus_, Aug 21 2005