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A111906 Numbers k such that fewer primes, among primes <= the largest prime dividing k, divide k than do not.

%I A111906 #18 Jun 23 2024 04:59:25
%S A111906 5,7,11,13,17,19,22,23,25,26,29,31,33,34,37,38,39,41,43,44,46,47,49,
%T A111906 51,52,53,55,57,58,59,61,62,65,67,68,69,71,73,74,76,77,79,82,83,85,86,
%U A111906 87,88,89,91,92,93,94,95,97,99,101,102,103,104,106,107,109,111,113,114,115
%N A111906 Numbers k such that fewer primes, among primes <= the largest prime dividing k, divide k than do not.
%H A111906 John Tyler Rascoe, <a href="/A111906/b111906.txt">Table of n, a(n) for n = 1..10000</a>
%e A111906 22 is included because 11 is the largest prime dividing 22. And of the primes <= 11 (2,3,5,7,11), 2 and 11 (2 primes) divide 22, but 3 and 5 and 7 (3 primes) do not divide 22.
%o A111906 (PARI) {m=115;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 A111906 (Python)
%o A111906 from itertools import count, islice
%o A111906 from sympy import sieve, factorint
%o A111906 def a_gen():
%o A111906     for n in count(3):
%o A111906         f = [sieve.search(i)[0] for i in factorint(n)]
%o A111906         if len(f) < (f[-1]+1)//2:
%o A111906             yield n
%o A111906 A111906_list = list(islice(a_gen(), 100)) # _John Tyler Rascoe_, Jun 22 2024
%Y A111906 Cf. A111905, A111907.
%K A111906 nonn
%O A111906 1,1
%A A111906 _Leroy Quet_, Aug 19 2005
%E A111906 More terms from _Klaus Brockhaus_, Aug 21 2005