cp's OEIS Frontend

A359080 Numbers k such that A246600(k) = A000005(k).

%I A359080 #25 Mar 20 2023 19:23:40
%S A359080 1,3,5,7,11,13,15,17,19,23,27,29,31,37,41,43,47,51,53,59,61,63,67,71,
%T A359080 73,79,83,85,89,95,97,101,103,107,109,111,113,119,123,125,127,131,137,
%U A359080 139,143,149,151,157,163,167,173,179,181,187,191,193,197,199,211,219
%N A359080 Numbers k such that A246600(k) = A000005(k).
%C A359080 Numbers k such that for all the divisors d of k the bitwise OR of k and d is equal to k (or equivalently, the bitwise AND of k and d is equal to d).
%C A359080 Subsequence of A102553. Terms of A102553 that are not in this sequence: 2, 135, 175, 243, 343, ... .
%C A359080 All the terms are odd since if k is even and d = 1 then bitor(k, 1) > k and thus A246600(k) < A000005(k).
%C A359080 All the odd primes are terms.
%C A359080 All the numbers of the form 2^k-1 (A000225) are terms.
%C A359080 Numbers k such that the bitwise OR(k, d_1, d_2, ..., d_m) = k, where d_1, ..., d_m are the divisors of k. - _Chai Wah Wu_, Dec 18 2022
%H A359080 Amiram Eldar, <a href="/A359080/b359080.txt">Table of n, a(n) for n = 1..10000</a>
%H A359080 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%H A359080 <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>.
%t A359080 s[n_] := DivisorSum[n, 1 &, BitAnd[n, #] == # &]; Select[Range[250], s[#] == DivisorSigma[0, #] &]
%o A359080 (PARI) is(n) = sumdiv(n, d, bitor(d, n) == n) == numdiv(n);
%o A359080 (Python)
%o A359080 from itertools import count, islice
%o A359080 from operator import ior
%o A359080 from functools import reduce
%o A359080 from sympy import divisors
%o A359080 def A359080_gen(startvalue=1):  # generator of terms >= startvalue
%o A359080     return filter(
%o A359080         lambda n: n | reduce(ior, divisors(n, generator=True)) == n,
%o A359080         count(max(startvalue, 1)),
%o A359080     )
%o A359080 A359080_list = list(islice(A359080_gen(), 20))  # _Chai Wah Wu_, Dec 18 2022
%o A359080 print(A359080_list)
%Y A359080 Subsequence of A102553.
%Y A359080 Subsequences: A000225, A065091.
%Y A359080 Cf. A000005, A246600, A359081, A359082, A359083.
%K A359080 nonn,base
%O A359080 1,2
%A A359080 _Amiram Eldar_, Dec 15 2022