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A090333 Nonprimes with no divisors >1 that are prefixes of other divisors in binary representation.

%I A090333 #12 Dec 16 2021 07:35:14
%S A090333 1,9,25,33,35,49,65,69,77,91,121,125,129,133,141,143,145,155,161,169,
%T A090333 209,247,259,265,267,287,289,295,299,301,305,319,323,329,341,343,361,
%U A090333 371,377,391,395,403,407,437,451,473,481,485,493,505,515,519,527,529,533
%N A090333 Nonprimes with no divisors >1 that are prefixes of other divisors in binary representation.
%C A090333 A090332 without primes.
%C A090333 Includes all members of A001248 except 4. - _Robert Israel_, Jul 08 2020
%H A090333 Robert Israel, <a href="/A090333/b090333.txt">Table of n, a(n) for n = 1..10000</a>
%p A090333 filter:= proc(n) local d,  i,j;
%p A090333   if isprime(n) then return false fi;
%p A090333   d:= numtheory:-divisors(n);
%p A090333   for i in d do
%p A090333     for j from 1 to ilog2(i)-1 do
%p A090333       if member(floor(i/2^j), d) then return false fi
%p A090333   od od;
%p A090333   true
%p A090333 end proc:
%p A090333 select(filter, [seq(i,i=1..1000,2)]); # _Robert Israel_, Jul 08 2020
%t A090333 filterQ[n_] := If[PrimeQ[n], False, Catch@Module[{d = Divisors[n], j}, Do[For[j = 1, j <= Floor@Log[2, i]-1, j++, If[MemberQ[d, Floor[i/2^j]], Throw[False]]], {i, d}]; True]];
%t A090333 Select[Range[1000], filterQ] (* _Jean-François Alcover_, Dec 16 2021, after _Robert Israel_ *)
%Y A090333 Cf. A001248, A090332.
%K A090333 nonn,base
%O A090333 1,2
%A A090333 _Reinhard Zumkeller_, Nov 26 2003
%E A090333 Missing term 121 inserted by _Robert Israel_, Jul 08 2020