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A111906
Numbers k such that fewer primes, among primes <= the largest prime dividing k, divide k than do not.
3
5, 7, 11, 13, 17, 19, 22, 23, 25, 26, 29, 31, 33, 34, 37, 38, 39, 41, 43, 44, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59, 61, 62, 65, 67, 68, 69, 71, 73, 74, 76, 77, 79, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 101, 102, 103, 104, 106, 107, 109, 111, 113, 114, 115
OFFSET
1,1
LINKS
EXAMPLE
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.
PROG
(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
(Python)
from itertools import count, islice
from sympy import sieve, factorint
def a_gen():
for n in count(3):
f = [sieve.search(i)[0] for i in factorint(n)]
if len(f) < (f[-1]+1)//2:
yield n
A111906_list = list(islice(a_gen(), 100)) # John Tyler Rascoe, Jun 22 2024
CROSSREFS
Sequence in context: A035035 A256387 A113909 * A348471 A101550 A320048
KEYWORD
nonn
AUTHOR
Leroy Quet, Aug 19 2005
EXTENSIONS
More terms from Klaus Brockhaus, Aug 21 2005
STATUS
approved