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

1,2

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A093653.

A058891 is a subsequence.

Sequence in context: A051934 A153915 A355581 * A281645 A351853 A224211

Adjacent sequences: A093702 A093703 A093704 * A093706 A093707 A093708

Keyword

easy,base,nonn

Author

Jason Earls, May 17 2004

Status

approved