%I #33 Oct 20 2024 02:07:54

%S 10010,100010,100110,110010,1000010,1000100,1000110,1001010,1001110,

%T 1010010,1100010,1100110,1110010,10000010,10000100,10000110,10001010,

%U 10001100,10001110,10010010,10010110,10011010,10011110,10100010,10100110,10110010,11000010,11000100,11000110,11001010,11001110,11010010,11100010,11100110,11110010,100000010,100000100

%N Even numbers n (written in binary) such that in base-2 lunar arithmetic, the sum of the divisors of n is a number containing a 0 (in binary).

%C As remarked in A188548, if n is even then most of the time A188548(n) = 111...111 (that is, a number of the form 2^k-1). This sequence lists the exceptions.

%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

%H D. Applegate, M. LeBrun, and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.html">Dismal Arithmetic</a>, J. Int. Seq. 14 (2011) # 11.9.8.

%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>

%e In base-2 lunar arithmetic, the divisors of 10010 are 1, 10, 1001 and 10010, whose sum is 11011.

%Y Cf. A188548, A067399. See A190150 and A190151 for the base-10 representation of these numbers.

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_, May 05 2011