A102554 Numbers k such that p <> (k AND p) for at least one prime-factor p.

4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 52, 54, 55, 56, 57, 58, 60, 62, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 86, 87, 88, 90, 91, 92, 93, 94, 96, 98, 99, 100, 102, 104

Offset: 1

Author

Reinhard Zumkeller, Jan 14 2005

Keywords

• nonn
• base

Comments

Numbers k such that A102550(k) < A001221(k).

Numbers k such that the bitwise OR of k and all prime factors of k is not equal to k. - Chai Wah Wu, Dec 18 2022

Crossrefs

Cf. A001221, A102550, A102553, A007088, A004676.

Programs

Maple

isA102554 := proc(n)
    local p;
    for p in numtheory[factorset](n) do
        if p <> ANDnos(p,n) then
            return true
        end if;
    end do:
    false ;
end proc:
for n from 1 to 500 do
    if isA102554(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Jan 20 2023

Python

from itertools import count, islice
from functools import reduce
from operator import ior
from sympy import primefactors
def A102554_gen(startvalue=2): # generator of terms >= startvalue
    return filter(lambda n:n|reduce(ior,primefactors(n))!=n,count(max(startvalue,2)))
A102554_list = list(islice(A102554_gen(),20)) # Chai Wah Wu, Dec 18 2022