A376617 - OEIS

%I #8 Sep 30 2024 12:50:01

%S 1,2,4,8,16,24,32,40,48,64,72,80,96,128,136,144,160,192,256,264,272,

%T 288,320,384,512,520,528,544,576,640,756,768,960,1024,1032,1040,1056,

%U 1088,1104,1152,1280,1296,1380,1472,1512,1536,1620,1656,1728,1840,1856,1920,1944

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

%C Numbers k such that A376615(k) = 0 or A376615(k) >= 4.

%H Amiram Eldar, <a href="/A376617/b376617.txt">Table of n, a(n) for n = 1..10000</a>

%e 24 is a term since 24/wt(24) = 12 is an integer, 12/wt(12) = 6 is an integer, and 6/wt(6) = 3 is an integer.

%t q[k_] := Module[{w = DigitCount[k, 2, 1], w2, m, n}, IntegerQ[m = k/w] && Divisible[m, w2 = DigitCount[m, 2, 1]] && Divisible[n = m/w2, DigitCount[n, 2, 1]]]; Select[Range[2000], q]

%o (PARI) s(n) = {my(w = hammingweight(n)); if(w == 1, 0, if(n % w, 1, 1 + s(n/w)));}

%o is(k) = {my(sk = s(k)); sk == 0 || sk >= 4;}

%Y Subsequence of A049445 and A376616.

%Y A000079 is a subsequence.

%Y Cf. A000120, A376615.

%K nonn,easy,base,new

%O 1,2

%A _Amiram Eldar_, Sep 30 2024