A093705 Numbers that are divisible by the total number of 1's in the binary expansions of all their divisors.

1, 2, 3, 6, 8, 24, 27, 45, 49, 54, 55, 77, 90, 98, 108, 110, 128, 154, 180, 189, 209, 216, 299, 324, 360, 378, 384, 392, 418, 425, 440, 448, 598, 616, 689, 765, 783, 850, 855, 864, 880, 891, 896, 931, 972, 1023, 1040, 1056, 1160, 1188, 1200, 1209, 1215, 1378

Offset: 1

Author

Jason Earls, May 17 2004

Keywords

• easy
• base
• nonn

Comments

Numbers of the form 2^(2^k-1) (A058891) are terms of this sequence since A093653(2^(2^k-1)) = 2^k. - Amiram Eldar, Oct 31 2020

Examples

			a(5) = 8 because the divisors of 8 in binary are: 1, 10, 100, 1000, with four 1's and 8/4 = 2.
		

Links

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

Crossrefs

Cf. A093653.

A058891 is a subsequence.

Programs

Magma

f:=func< n|&+[&+Intseq(d,2):d in Divisors(n)]>; [k:k in [1..1500]| k mod f(k) eq 0]; // Marius A. Burtea, Dec 16 2019

Mathematica

Select[Range[1500], Divisible[#, Plus @@ DigitCount[Divisors[#], 2, 1]] &] (* Amiram Eldar, Dec 16 2019 *)