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

2, 4, 6, 8, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 42, 45, 48, 50, 54, 60, 64, 66, 70, 72, 75, 80, 84, 90, 96, 100, 105, 108, 110, 120, 126, 128, 132, 135, 140, 144, 150, 154, 160, 162, 165, 168, 180, 192, 198, 200, 210, 216, 220, 225, 231, 240, 250, 252, 256, 264

Offset: 1

Author

Leroy Quet, Aug 19 2005

Keywords

• nonn

Examples

			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.
		

Links

• John Tyler Rascoe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A111906, A111907.

Programs

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

Python

from itertools import count, islice
from sympy import sieve, factorint
def a_gen():
    for n in count(2):
        f = [sieve.search(i)[0] for i in factorint(n)]
        if len(f) > f[-1]//2:
            yield n
A111905_list = list(islice(a_gen(), 100)) # John Tyler Rascoe, Jun 22 2024

Extensions

More terms from Klaus Brockhaus, Aug 21 2005