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

%I A102553 #21 Dec 19 2022 03:32:47
%S A102553 1,2,3,5,7,11,13,15,17,19,23,27,29,31,37,41,43,47,51,53,59,61,63,67,
%T A102553 71,73,79,83,85,89,95,97,101,103,107,109,111,113,119,123,125,127,131,
%U A102553 135,137,139,143,149,151,157,163,167,173,175,179,181,187,191,193,197,199
%N A102553 Numbers k such that for all prime-factors p: p = (k AND p), bitwise.
%C A102553 Numbers k such that A102550(k) = A001221(k).
%C A102553 Apart from first term, subsequence of A102552;
%C A102553 A000040 is a subsequence.
%C A102553 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
%H A102553 Michael De Vlieger, <a href="/A102553/b102553.txt">Table of n, a(n) for n = 1..10000</a>
%t A102553 okQ[n_] := AllTrue[FactorInteger[n][[All, 1]], # == BitAnd[n, #]&];
%t A102553 Select[Range[200], okQ] (* _Jean-François Alcover_, Nov 16 2021 *)
%o A102553 (Python)
%o A102553 from itertools import count, islice
%o A102553 from operator import ior
%o A102553 from functools import reduce
%o A102553 from sympy import primefactors
%o A102553 def A102553_gen(startvalue=1): # generator of terms >= startvalue
%o A102553     return filter(lambda n:n == 1 or n|reduce(ior,primefactors(n))==n,count(max(startvalue,1)))
%o A102553 A102553_list = list(islice(A102553_gen(),20)) # _Chai Wah Wu_, Dec 18 2022
%Y A102553 Cf. A000040, A001221, A102550, A102552, A102554, A007088, A004676.
%K A102553 nonn,base
%O A102553 1,2
%A A102553 _Reinhard Zumkeller_, Jan 14 2005