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 A113705 #12 May 25 2017 04:21:08
%S A113705 1,10,110,1010,10110,100010,1001110,10000010,100010110,1000001010,
%T A113705 10000100110,100000000010,1000001011110,10000000000010,
%U A113705 100000010000110,1000000000101010,10000000100010110,100000000000000010,1000000001001001110,10000000000000000010,100000000010000110110
%N A113705 Inverse Moebius transform of powers of 10.
%C A113705 A055895 to base 2.
%C A113705 The triangle formed by stacking the reversals of a(n) is A113704.
%C A113705 Using decimal positional notation, write a 1 at position d for all divisors d of n. All other digits are zeros and leading zeros are not permitted. - _Michael De Vlieger_, May 24 2017
%H A113705 Michael De Vlieger, <a href="/A113705/b113705.txt">Table of n, a(n) for n = 0..999</a>
%F A113705 a(n) = Sum_{k=0..n} if(mod(n, k)=0, 10^k, 0).
%F A113705 G.f.: Sum_{k>=1} 10^k*x^k/(1 - x^k). - _Ilya Gutkovskiy_, May 23 2017
%e A113705 From _Michael De Vlieger_, May 24 2017: (Start)
%e A113705 First 20 terms of a(n), replacing zeros with "." to more clearly show positions of 1s in positions corresponding to terms in row n of A027750. This chart also pertains to terms of A055895 written in binary.
%e A113705 n a(n) A027750(n)
%e A113705 ---------------------------------------
%e A113705 0: 1 {}
%e A113705 1: 1. 1
%e A113705 2: 11. 1,2
%e A113705 3: 1.1. 1,3
%e A113705 4: 1.11. 1,2,4
%e A113705 5: 1...1. 1,5
%e A113705 6: 1..111. 1,2,3,6
%e A113705 7: 1.....1. 1,7
%e A113705 8: 1...1.11. 1,2,4,8
%e A113705 9: 1.....1.1. 1,3,9
%e A113705 10: 1....1..11. 1,2,5,10
%e A113705 11: 1.........1. 1,11
%e A113705 12: 1.....1.1111. 1,2,3,4,6,12
%e A113705 13: 1...........1. 1,13
%e A113705 14: 1......1....11. 1,2,7,14
%e A113705 15: 1.........1.1.1. 1,3,5,15
%e A113705 16: 1.......1...1.11. 1,2,4,8,16
%e A113705 17: 1...............1. 1,17
%e A113705 18: 1........1..1..111. 1,2,3,6,9,18
%e A113705 19: 1.................1. 1,19
%e A113705 20: 1.........1....11.11. 1,2,4,5,10,20 (End)
%t A113705 Table[If[n == 0, 1, Total[10^Divisors[n]]], {n, 0, 20}] (* or *)
%t A113705 Table[If[n == 0, 1, Sum[If[Mod[n, k] == 0, 10^k, 0], {k, n}]], {n, 0,
%t A113705 20}] (* or *)
%t A113705 Table[Boole[n == 0] + Total@ MapIndexed[Boole[Divisible[n, #1]]*10^First@ #2 &, Range@ n], {n, 0, 20}] (* or *)
%t A113705 Table[If[n == 0, 1, Function[d, FromDigits @Reverse@ ReplacePart[#, Map[# + 1 -> 1 &, d]] &@ ConstantArray[0, n + 1]]@ Divisors@ n], {n, 0, 20}]
%t A113705 (* _Michael De Vlieger_, May 24 2017 *)
%o A113705 (PARI) a(n) = if (n==0, 1, sum(k=1, n, if (! (n % k), 10^k))); \\ _Michel Marcus_, May 23 2017
%Y A113705 Cf. A027750, A055895, A113704.
%K A113705 easy,nonn
%O A113705 0,2
%A A113705 _Paul Barry_, Nov 05 2005