cp's OEIS Frontend

A090332 Numbers with no divisors >1 that are prefixes of other divisors in binary representation.

%I A090332 #13 Dec 16 2021 07:38:13
%S A090332 1,2,3,5,7,9,11,13,17,19,23,25,29,31,33,35,37,41,43,47,49,53,59,61,65,
%T A090332 67,69,71,73,77,79,83,89,91,97,101,103,107,109,113,121,125,127,129,
%U A090332 131,133,137,139,141,143,145,149,151,155,157,161,163,167,169,173,179,181
%N A090332 Numbers with no divisors >1 that are prefixes of other divisors in binary representation.
%C A090332 A090333 is a subsequence.
%C A090332 Complement of A090334.
%C A090332 Divisors >1 of a(n) in binary representation form a prefix code.
%H A090332 Robert Israel, <a href="/A090332/b090332.txt">Table of n, a(n) for n = 1..10000</a>
%F A090332 A090330(a(n)) = 0.
%F A090332 A090331(a(n)) = 1.
%e A090332 Divisors >1 of a(188)=637: {7,13,49,91,637}, in binary: {111, 1101, 110001, 1011011, 1001111101}.
%p A090332 filter:= proc(n) local d,  i,j;
%p A090332   d:= numtheory:-divisors(n);
%p A090332   for i in d do
%p A090332     for j from 1 to ilog2(i)-1 do
%p A090332       if member(floor(i/2^j), d) then return false fi
%p A090332   od od;
%p A090332   true
%p A090332 end proc:
%p A090332 select(filter, [$1..200]); # _Robert Israel_, Jul 08 2020
%t A090332 filterQ[n_] := Catch@Module[{d = Divisors[n], j}, Do[
%t A090332      For[j = 1, j <= Floor@Log[2, i]-1, j++,
%t A090332      If[MemberQ[d, Floor[i/2^j]], Throw[False]]], {i, d}];
%t A090332      True];
%t A090332 Select[Range[200], filterQ] (* _Jean-François Alcover_, Dec 15 2021, after _Robert Israel_ *)
%Y A090332 Cf. A090330, A090331, A090333, A090335, A088862.
%K A090332 nonn,base
%O A090332 1,2
%A A090332 _Reinhard Zumkeller_, Nov 26 2003
%E A090332 Missing term 121 inserted by _Robert Israel_, Jul 08 2020