The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #9 Jun 18 2021 01:16:05
%S 132061,138421,151427,532393,545269,546407,557983,559609,568801,
%T 570709,573193,579013,590687,595853,599707,604873,610777,624553,
%U 630293,635213,2102767,2105063,2109383,2111339,2123677,2128187,2129081,2129609,2143961,2149753,2151131,2151661
%N Composite numbers whose divisors that are larger than 1 are all digitally balanced numbers in base 2 (A031443).
%C The prime numbers with this property are the digitally balanced primes (A066196).
%C All the terms are odd, since if k is an even digitally balanced number then its divisor k/2 is not digitally balanced (since it has one fewer 0 in its binary expansion).
%C Apparently most of the terms are semiprimes (A001358) with 4 divisors.
%C Terms with 3 divisors, i.e., squares of primes: 145178401 = 12049^2, 155575729 = 12473^2, ...
%C The least term with more than 4 divisors is 8897396239 = 163 * 929 * 58757, with 8 divisors.
%C The least term with 6 divisors is 8923691369 = 41 * 14753^2.
%e 132061 is a term since its divisors that are larger than 1 are {41, 3221, 132061}, and their binary representations are {101001, 110010010101, 100000001111011101}. Each one has an equal number of 0's and 1's.
%t balQ[n_] := Module[{d = IntegerDigits[n, 2], m}, EvenQ @ (m = Length @ d) && Count[d, 1] == m/2]; Select[Range[9,10^6,2], CompositeQ[#] && AllTrue[Rest@Divisors[#], balQ] &]
%Y Subsequence of A031443.
%Y Cf. A066196.
%K nonn,base
%O 1,1
%A _Amiram Eldar_, Jun 17 2021