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A175381 A positive integer of n is included if all positive integers that, when written in binary, occur as substrings in binary n divide n. 2

%I #25 Nov 25 2016 05:28:28

%S 1,2,3,4,6,8,10,12,16,20,24,32,36,40,48,64,72,80,96,128,136,144,160,

%T 192,256,272,288,320,384,512,528,544,576,640,768,1024,1056,1088,1152,

%U 1280,1536,2048,2080,2112,2176,2304,2560,3072,4096,4160,4224,4352,4608

%N A positive integer of n is included if all positive integers that, when written in binary, occur as substrings in binary n divide n.

%C This is the complement of sequence A175382.

%C This sequence is infinite (because it contains all powers of 2).

%C The union of powers of 2 and numbers of the form 2^n + 2^k, where floor(n/2) <= k < n. - _Ivan Neretin_, Nov 24 2016

%H Ivan Neretin, <a href="/A175381/b175381.txt">Table of n, a(n) for n = 1..10000</a>

%e 20 in binary is 10100. The positive integers that, when written in binary, occur as substrings in 10100 are: 1 (1 in binary), 2 (10 in binary), 4 (100 in binary), 5 (101 in binary), 10 (1010 in binary), and 20 (10100 in binary.) Since 1, 2, 4, 5, 10, and 20 each are a divisor of 20, then 20 is in this sequence.

%t mx = 12; Union[2^Range[0, mx], Flatten@Table[2^n + 2^k, {n, 0, mx}, {k, Quotient[n, 2], n - 1}]] (* _Ivan Neretin_, Nov 24 2016 *)

%Y Cf. A175382.

%K base,nonn

%O 1,2

%A _Leroy Quet_, Apr 24 2010

%E Spelling corrected by _Jason G. Wurtzel_, Sep 04 2010

%E a(11)-a(53) from _Lars Blomberg_, May 05 2011

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Last modified March 29 09:14 EDT 2024. Contains 371268 sequences. (Running on oeis4.)