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A329936 Binary hoax numbers: composite numbers k such that sum of bits of k equals the sum of bits of the distinct prime divisors of k.

%I A329936 #19 Nov 29 2019 03:25:40
%S A329936 4,8,9,15,16,32,45,49,50,51,55,64,75,85,100,117,126,128,135,153,159,
%T A329936 162,171,185,190,200,205,207,215,222,225,238,246,249,252,253,256,287,
%U A329936 303,319,324,333,338,350,369,374,378,380,400,407,438,442,444,469,471
%N A329936 Binary hoax numbers: composite numbers k such that sum of bits of k equals the sum of bits of the distinct prime divisors of k.
%C A329936 Analogous to A278909 (binary Smith numbers) as A019506 (hoax numbers) is analogous to A006753 (Smith numbers).
%C A329936 Includes all the powers of 2 except for 1 and 2.
%H A329936 Amiram Eldar, <a href="/A329936/b329936.txt">Table of n, a(n) for n = 1..10000</a>
%e A329936 4 = 2^2 is in the sequence since the binary representation of 4 is 100 and 1 + 0 + 0 = 1, and the binary representation of 2 is 10 and 1 + 0 = 1.
%p A329936 filter:= proc(n)
%p A329936 if isprime(n) then return false fi;
%p A329936 convert(convert(n,base,2),`+`) = add(convert(convert(t,base,2),`+`),t=numtheory:-factorset(n))
%p A329936 end proc:
%p A329936 select(filter, [$2..1000]); # _Robert Israel_, Nov 28 2019
%t A329936 binWt[n_] := Total @ IntegerDigits[n, 2]; binHoaxQ[n_] := CompositeQ[n] && Total[binWt /@ FactorInteger[n][[;; , 1]]] == binWt[n]; Select[Range[500], binHoaxQ]
%o A329936 (PARI) is(n)= my(f=factor(n)[,1]); sum(i=1,#f, hammingweight(f[i]))==hammingweight(n) && !isprime(n) \\ _Charles R Greathouse IV_, Nov 28 2019
%Y A329936 Cf. A006753, A019506, A278909.
%K A329936 nonn,base
%O A329936 1,1
%A A329936 _Amiram Eldar_, Nov 24 2019