A102553 - OEIS

%I #21 Dec 19 2022 03:32:47

%S 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 71,73,79,83,85,89,95,97,101,103,107,109,111,113,119,123,125,127,131,

%U 135,137,139,143,149,151,157,163,167,173,175,179,181,187,191,193,197,199

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

%C Numbers k such that A102550(k) = A001221(k).

%C Apart from first term, subsequence of A102552;

%C A000040 is a subsequence.

%C 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 Michael De Vlieger, <a href="/A102553/b102553.txt">Table of n, a(n) for n = 1..10000</a>

%t okQ[n_] := AllTrue[FactorInteger[n][[All, 1]], # == BitAnd[n, #]&];

%t Select[Range[200], okQ] (* _Jean-François Alcover_, Nov 16 2021 *)

%o (Python)

%o from itertools import count, islice

%o from operator import ior

%o from functools import reduce

%o from sympy import primefactors

%o def A102553_gen(startvalue=1): # generator of terms >= startvalue

%o     return filter(lambda n:n == 1 or n|reduce(ior,primefactors(n))==n,count(max(startvalue,1)))

%o A102553_list = list(islice(A102553_gen(),20)) # _Chai Wah Wu_, Dec 18 2022

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

%K nonn,base

%O 1,2

%A _Reinhard Zumkeller_, Jan 14 2005