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

1,2

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A331635 A320055 A072697 * A069161 A328603 A304713

Adjacent sequences: A102550 A102551 A102552 * A102554 A102555 A102556

Keyword

nonn,base

Author

Reinhard Zumkeller, Jan 14 2005

Status

approved