A102553 Numbers k such that for all prime-factors p: p = (k AND p), bitwise.

1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 27, 29, 31, 37, 41, 43, 47, 51, 53, 59, 61, 63, 67, 71, 73, 79, 83, 85, 89, 95, 97, 101, 103, 107, 109, 111, 113, 119, 123, 125, 127, 131, 135, 137, 139, 143, 149, 151, 157, 163, 167, 173, 175, 179, 181, 187, 191, 193, 197, 199

Offset: 1

Author

Reinhard Zumkeller, Jan 14 2005

Keywords

• nonn
• base

Comments

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

Apart from first term, subsequence of A102552;

A000040 is a subsequence.

Numbers k such that the bitwise OR of k with all prime divisors of k is equal to k. - Chai Wah Wu, Dec 18 2022

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001221, A102550, A102552, A102554, A007088, A004676.

Programs

Mathematica

okQ[n_] := AllTrue[FactorInteger[n][[All, 1]], # == BitAnd[n, #]&];
Select[Range[200], okQ] (* Jean-François Alcover, Nov 16 2021 *)

Python

from itertools import count, islice
from operator import ior
from functools import reduce
from sympy import primefactors
def A102553_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:n == 1 or n|reduce(ior,primefactors(n))==n,count(max(startvalue,1)))
A102553_list = list(islice(A102553_gen(),20)) # Chai Wah Wu, Dec 18 2022