A376618 - OEIS

%I #7 Sep 30 2024 12:50:11

%S 1,345,405,775,1305,1425,1435,1605,2125,2325,2485,2765,2825,4235,4305,

%T 4459,4655,4725,5085,5145,5607,5625,5929,6223,6405,7515,7623,8145,

%U 10625,11151,11835,12325,12355,12425,13527,13825,13995,14805,16695,18445,20505,20625,20925

%N Odd binary Niven numbers (A144302) k such that k/wt(k) is also an odd binary Niven number, where wt(k) = A000120(k) is the binary weight of k.

%C If m is a term then 2^k * m is a term of A376616 for all k >= 0.

%H Amiram Eldar, <a href="/A376618/b376618.txt">Table of n, a(n) for n = 1..10000</a>

%e 345 is a term since it is odd, 345/wt(345) = 69 is an integer, and 69/wt(69) = 23 is an integer.

%t q[k_] := Module[{w = DigitCount[k, 2, 1]}, Divisible[k, w] && Divisible[k/w, DigitCount[k/w, 2, 1]]]; Select[Range[1, 21000, 2], q]

%o (PARI) is(k) = if(!(k % 2), 0, my(w = hammingweight(k)); !(k % w) && !((k/w) % hammingweight(k/w)));

%Y Intersection of A005408 and A376616.

%Y Subsequence of A049445 and A144302.

%Y Cf. A000120.

%K nonn,easy,base,new

%O 1,2

%A _Amiram Eldar_, Sep 30 2024