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A363787 Primitive binary Niven numbers: binary Niven numbers (A049445) that are not twice another binary Niven number.

%I A363787 #10 Jun 24 2023 13:22:08
%S A363787 1,6,10,18,21,34,55,60,66,69,81,92,108,115,116,126,130,155,156,172,
%T A363787 180,185,204,205,212,222,228,246,258,261,273,284,285,295,300,308,318,
%U A363787 321,332,340,345,355,356,366,378,395,396,404,405,414,420,425,438,452,462
%N A363787 Primitive binary Niven numbers: binary Niven numbers (A049445) that are not twice another binary Niven number.
%C A363787 Every binary Niven number is of the form m*2^k, where m is a term of this sequence and k >= 0.
%C A363787 Includes all the odd binary Niven numbers (A144302).
%C A363787 This sequence is infinite. E.g., 16^k + 4^k + 1 is a term for all k >= 1.
%H A363787 Amiram Eldar, <a href="/A363787/b363787.txt">Table of n, a(n) for n = 1..10000</a>
%e A363787 6 is a term as 6 is a binary Niven number and 6/2 = 3 is not a binary Niven number.
%t A363787 binNivQ[n_] := Divisible[n, DigitCount[n, 2, 1]]; q[n_] := binNivQ[n] && ! (EvenQ[n] && binNivQ[n/2]); Select[Range[500], q]
%o A363787 (PARI) isbinniv(n) = !(n % hammingweight(n));
%o A363787 is(n) = isbinniv(n) && !(!(n%2) && isbinniv(n/2));
%Y A363787 Subsequence of A049445.
%Y A363787 Disjoint union of A144302 and A363788.
%Y A363787 A363789 is a subsequence.
%Y A363787 Cf. A356349 (decimal analog).
%K A363787 nonn,easy,base
%O A363787 1,2
%A A363787 _Amiram Eldar_, Jun 22 2023