A376618 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.

1, 345, 405, 775, 1305, 1425, 1435, 1605, 2125, 2325, 2485, 2765, 2825, 4235, 4305, 4459, 4655, 4725, 5085, 5145, 5607, 5625, 5929, 6223, 6405, 7515, 7623, 8145, 10625, 11151, 11835, 12325, 12355, 12425, 13527, 13825, 13995, 14805, 16695, 18445, 20505, 20625, 20925

Offset: 1

Author

Amiram Eldar, Sep 30 2024

Keywords

• nonn
• easy
• base

Comments

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

Examples

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

Links

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

Crossrefs

Intersection of A005408 and A376616.

Subsequence of A049445 and A144302.

Cf. A000120.

Programs

Mathematica

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]

PARI

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