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A093705 Numbers that are divisible by the total number of 1's in the binary expansions of all their divisors. 9
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
easy,base,nonn
AUTHOR
Jason Earls, May 17 2004
STATUS
approved

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Last modified March 28 11:44 EDT 2024. Contains 371241 sequences. (Running on oeis4.)