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

1,1

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

Links

Table of n, a(n) for n=1..70.

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

Prog

(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

Crossrefs

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

Sequence in context: A060679 A051234 A327776 * A371862 A070810 A227180

Adjacent sequences: A102551 A102552 A102553 * A102555 A102556 A102557

Keyword

nonn,base

Author

Reinhard Zumkeller, Jan 14 2005

Status

approved