A376616 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.

1, 2, 4, 8, 12, 16, 20, 24, 32, 36, 40, 48, 64, 68, 72, 80, 96, 126, 128, 132, 136, 144, 160, 192, 240, 252, 256, 260, 264, 272, 276, 288, 320, 324, 345, 368, 384, 405, 414, 432, 460, 464, 480, 486, 504, 512, 516, 520, 528, 544, 552, 576, 624, 640, 648, 688, 690

Offset: 1

Author

Amiram Eldar, Sep 30 2024

Keywords

• nonn
• easy
• base

Comments

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

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

Examples

			12 is a term since 12/wt(12) = 6 is an integer and also 6/wt(6) = 3 is an integer.
		

Links

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

Crossrefs

Subsequence of A049445.

Subsequences: A000079, A376617, A376618.

Cf. A000120, A376615.

Programs

Mathematica

q[k_] := Module[{w = DigitCount[k, 2, 1]}, Divisible[k, w] && Divisible[k/w, DigitCount[k/w, 2, 1]]]; Select[Range[1000], q]

PARI

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