A363787 Primitive binary Niven numbers: binary Niven numbers (A049445) that are not twice another binary Niven number.

1, 6, 10, 18, 21, 34, 55, 60, 66, 69, 81, 92, 108, 115, 116, 126, 130, 155, 156, 172, 180, 185, 204, 205, 212, 222, 228, 246, 258, 261, 273, 284, 285, 295, 300, 308, 318, 321, 332, 340, 345, 355, 356, 366, 378, 395, 396, 404, 405, 414, 420, 425, 438, 452, 462

Offset: 1

Author

Amiram Eldar, Jun 22 2023

Keywords

• nonn
• easy
• base

Comments

Every binary Niven number is of the form m*2^k, where m is a term of this sequence and k >= 0.

Includes all the odd binary Niven numbers (A144302).

This sequence is infinite. E.g., 16^k + 4^k + 1 is a term for all k >= 1.

Examples

			6 is a term as 6 is a binary Niven number and 6/2 = 3 is not a binary Niven number.
		

Links

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

Crossrefs

Subsequence of A049445.

Disjoint union of A144302 and A363788.

A363789 is a subsequence.

Cf. A356349 (decimal analog).

Programs

Mathematica

binNivQ[n_] := Divisible[n, DigitCount[n, 2, 1]]; q[n_] := binNivQ[n] && ! (EvenQ[n] && binNivQ[n/2]); Select[Range[500], q]

PARI

isbinniv(n) = !(n % hammingweight(n));
is(n) = isbinniv(n) && !(!(n%2) && isbinniv(n/2));