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A111905
Numbers k such that more primes, among primes <= the largest prime dividing k, divide k than do not.
3
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
1,1
LINKS
EXAMPLE
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.
PROG
(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
CROSSREFS
Sequence in context: A264986 A140955 A386213 * A255385 A187412 A187473
KEYWORD
nonn
AUTHOR
Leroy Quet, Aug 19 2005
EXTENSIONS
More terms from Klaus Brockhaus, Aug 21 2005
STATUS
approved