A376617 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.

1, 2, 4, 8, 16, 24, 32, 40, 48, 64, 72, 80, 96, 128, 136, 144, 160, 192, 256, 264, 272, 288, 320, 384, 512, 520, 528, 544, 576, 640, 756, 768, 960, 1024, 1032, 1040, 1056, 1088, 1104, 1152, 1280, 1296, 1380, 1472, 1512, 1536, 1620, 1656, 1728, 1840, 1856, 1920, 1944

Offset: 1

Author

Amiram Eldar, Sep 30 2024

Keywords

• nonn
• easy
• base

Comments

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A049445 and A376616.

A000079 is a subsequence.

Cf. A000120, A376615.

Programs

Mathematica

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]

PARI

s(n) = {my(w = hammingweight(n)); if(w == 1, 0, if(n % w, 1, 1 + s(n/w)));}
is(k) = {my(sk = s(k)); sk == 0 || sk >= 4;}