This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A188548 #40 Apr 14 2021 01:17:05 %S A188548 1,11,11,111,101,111,111,1111,1001,1111,1011,1111,1101,1111,1111, %T A188548 11111,10001,11011,10011,11111,10101,11111,10111,11111,11001,11111, %U A188548 11011,11111,11101,11111,11111,111111,100001,110011,100011,111111,100101,110111,100111,111111,101001,111111,101011,111111,101101,111111,101111,111111,110001,111011,110011,111111 %N A188548 The sum of the divisors of n in base-2 lunar arithmetic. %C A188548 More precisely, in base-2 lunar arithmetic, the lunar sum of the lunar divisors of the n-th nonzero binary number. %C A188548 Theorem: a(n) = binary representation of n iff n is odd. %H A188548 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 A188548 N. J. A. Sloane, <a href="/A188548/a188548.txt">Table giving n (written in base 10), n (written in base 2), a(n) (written in base 2), a(n) (written in base 10)</a> %H A188548 <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a> %e A188548 The 4th binary number is 100 which has lunar divisors 1, 10, 100, whose lunar sum is 111, so a(4)=111. %e A188548 The 5th binary number is 101 which has lunar divisors 1 and 101, whose lunar sum is 101, so a(5)=101. %e A188548 It might be tempting to conjecture that if n is even then a(n) = 111...111, but a(18)=11011 shows that this is false (see A190149). %Y A188548 Cf. A067399 (number of divisors), A190149, A190632. %K A188548 nonn,base %O A188548 1,2 %A A188548 _N. J. A. Sloane_, Apr 04 2011