A376616 - OEIS

%I #7 Sep 30 2024 12:49:50

%S 1,2,4,8,12,16,20,24,32,36,40,48,64,68,72,80,96,126,128,132,136,144,

%T 160,192,240,252,256,260,264,272,276,288,320,324,345,368,384,405,414,

%U 432,460,464,480,486,504,512,516,520,528,544,552,576,624,640,648,688,690

%N Binary Niven numbers (A049445) k such that k/wt(k) is also a binary Niven number, where wt(k) = A000120(k) is the binary weight of k.

%C Numbers k such that A376615(k) = 0 or A376615(k) >= 3.

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

%H Amiram Eldar, <a href="/A376616/b376616.txt">Table of n, a(n) for n = 1..10000</a>

%e 12 is a term since 12/wt(12) = 6 is an integer and also 6/wt(6) = 3 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[1000], q]

%o (PARI) is(k) = {my(w = hammingweight(k)); !(k % w) && !((k/w) % hammingweight(k/w));}

%Y Subsequence of A049445.

%Y Subsequences: A000079, A376617, A376618.

%Y Cf. A000120, A376615.

%K nonn,easy,base

%O 1,2

%A _Amiram Eldar_, Sep 30 2024