A363691 Odd numbers k such that A246600(k) = 2.

3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 29, 31, 33, 35, 37, 41, 43, 47, 49, 53, 57, 59, 61, 65, 67, 69, 71, 73, 77, 79, 81, 83, 89, 91, 93, 97, 101, 103, 105, 107, 109, 113, 115, 117, 121, 127, 129, 131, 133, 137, 139, 141, 145, 149, 151, 155, 157, 161, 163, 167

Offset: 1

Author

Amiram Eldar, Jun 16 2023

Keywords

• nonn
• base
• easy

Comments

Odd numbers k that have exactly 2 divisors d such that the bitwise AND of k and d is equal to d, or equivalently, the bitwise OR of k and d is equal to k. These two divisors are 1 and k.

The terms of this sequence are the primitive terms of A363690: If m is a term, then 2^k*m is a term of A363690 for all k >= 0.

Includes all the odd primes (A065091), and all the squares of odd primes (A001248 \ {4}).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001248, A065091, A246600, A363690.

Programs

Mathematica

q[n_] := DivisorSum[n, Boole[BitOr[#, n] == n] &] == 2; Select[Range[1, 200, 2], q]

PARI

is(n) = n % 2 && sumdiv(n, d, bitor(d, n) == n) == 2;

Python

from itertools import count, islice
from sympy import divisors
def A363691_gen(startvalue=3): # generator of terms >= startvalue
    return filter(lambda n:all(d==1 or d==n or n|d!=n for d in divisors(n,generator=True)),count(max(startvalue,3)|1,2))
A363691_list = list(islice(A363691_gen(),20)) # Chai Wah Wu, Jun 20 2023