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

1,2

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.

Links

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

Example

12 is a term since 12/wt(12) = 6 is an integer and also 6/wt(6) = 3 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[1000], q]

Prog

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

Crossrefs

Subsequence of A049445.

Subsequences: A000079, A376617, A376618.

Cf. A000120, A376615.

Sequence in context: A364056 A010066 A180490 * A160408 A221707 A186146

Adjacent sequences: A376613 A376614 A376615 * A376617 A376618 A376619

Keyword

nonn,easy,base

Author

Amiram Eldar, Sep 30 2024

Status

approved