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

1,2

Comments

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

Links

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

Example

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

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]

Prog

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

Crossrefs

Intersection of A005408 and A376616.

Subsequence of A049445 and A144302.

Cf. A000120.

Sequence in context: A178191 A172934 A172952 * A306670 A251819 A251812

Adjacent sequences: A376615 A376616 A376617 * A376619 A376620 A376621

Keyword

nonn,easy,base,new

Author

Amiram Eldar, Sep 30 2024

Status

approved