cp's OEIS Frontend

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

%I A363691 #13 Jun 21 2023 06:47:18
%S A363691 3,5,7,9,11,13,17,19,21,23,25,29,31,33,35,37,41,43,47,49,53,57,59,61,
%T A363691 65,67,69,71,73,77,79,81,83,89,91,93,97,101,103,105,107,109,113,115,
%U A363691 117,121,127,129,131,133,137,139,141,145,149,151,155,157,161,163,167
%N A363691 Odd numbers k such that A246600(k) = 2.
%C A363691 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.
%C A363691 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.
%C A363691 Includes all the odd primes (A065091), and all the squares of odd primes (A001248 \ {4}).
%H A363691 Amiram Eldar, <a href="/A363691/b363691.txt">Table of n, a(n) for n = 1..10000</a>
%t A363691 q[n_] := DivisorSum[n, Boole[BitOr[#, n] == n] &] == 2; Select[Range[1, 200, 2], q]
%o A363691 (PARI) is(n) = n % 2 && sumdiv(n, d, bitor(d, n) == n) == 2;
%o A363691 (Python)
%o A363691 from itertools import count, islice
%o A363691 from sympy import divisors
%o A363691 def A363691_gen(startvalue=3): # generator of terms >= startvalue
%o A363691     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))
%o A363691 A363691_list = list(islice(A363691_gen(),20)) # _Chai Wah Wu_, Jun 20 2023
%Y A363691 Cf. A001248, A065091, A246600, A363690.
%K A363691 nonn,base,easy
%O A363691 1,1
%A A363691 _Amiram Eldar_, Jun 16 2023