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

1,2

Comments

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

Links

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

Example

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.

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]

Prog

(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; }

Crossrefs

Subsequence of A049445 and A376616.

A000079 is a subsequence.

Cf. A000120, A376615.

Sequence in context: A072874 A160158 A010072 * A318654 A375979 A333994

Adjacent sequences: A376614 A376615 A376616 * A376618 A376619 A376620

Keyword

nonn,easy,base,new

Author

Amiram Eldar, Sep 30 2024

Status

approved