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A102554 Numbers k such that p <> (k AND p) for at least one prime-factor p.

%I A102554 #11 Jan 20 2023 08:23:31
%S A102554 4,6,8,9,10,12,14,16,18,20,21,22,24,25,26,28,30,32,33,34,35,36,38,39,
%T A102554 40,42,44,45,46,48,49,50,52,54,55,56,57,58,60,62,64,65,66,68,69,70,72,
%U A102554 74,75,76,77,78,80,81,82,84,86,87,88,90,91,92,93,94,96,98,99,100,102,104
%N A102554 Numbers k such that p <> (k AND p) for at least one prime-factor p.
%C A102554 Numbers k such that A102550(k) < A001221(k).
%C A102554 Numbers k such that the bitwise OR of k and all prime factors of k is not equal to k. - _Chai Wah Wu_, Dec 18 2022
%p A102554 isA102554 := proc(n)
%p A102554     local p;
%p A102554     for p in numtheory[factorset](n) do
%p A102554         if p <> ANDnos(p,n) then
%p A102554             return true
%p A102554         end if;
%p A102554     end do:
%p A102554     false ;
%p A102554 end proc:
%p A102554 for n from 1 to 500 do
%p A102554     if isA102554(n) then
%p A102554         printf("%d,",n) ;
%p A102554     end if;
%p A102554 end do: # _R. J. Mathar_, Jan 20 2023
%o A102554 (Python)
%o A102554 from itertools import count, islice
%o A102554 from functools import reduce
%o A102554 from operator import ior
%o A102554 from sympy import primefactors
%o A102554 def A102554_gen(startvalue=2): # generator of terms >= startvalue
%o A102554     return filter(lambda n:n|reduce(ior,primefactors(n))!=n,count(max(startvalue,2)))
%o A102554 A102554_list = list(islice(A102554_gen(),20)) # _Chai Wah Wu_, Dec 18 2022
%Y A102554 Cf. A001221, A102550, A102553, A007088, A004676.
%K A102554 nonn,base
%O A102554 1,1
%A A102554 _Reinhard Zumkeller_, Jan 14 2005