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Numbers that are divisible by the total number of 1's in the binary expansions of all their divisors.
9

%I #16 Sep 08 2022 08:45:13

%S 1,2,3,6,8,24,27,45,49,54,55,77,90,98,108,110,128,154,180,189,209,216,

%T 299,324,360,378,384,392,418,425,440,448,598,616,689,765,783,850,855,

%U 864,880,891,896,931,972,1023,1040,1056,1160,1188,1200,1209,1215,1378

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

%C 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

%H Amiram Eldar, <a href="/A093705/b093705.txt">Table of n, a(n) for n = 1..10000</a>

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

%t Select[Range[1500], Divisible[#, Plus @@ DigitCount[Divisors[#], 2, 1]] &] (* _Amiram Eldar_, Dec 16 2019 *)

%o (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

%Y Cf. A093653.

%Y A058891 is a subsequence.

%K easy,base,nonn

%O 1,2

%A _Jason Earls_, May 17 2004