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 A135656 #7 Mar 11 2014 01:34:11 %S A135656 11,1110,11111000,111111100000,111111111111100000000000, %T A135656 11111111111111111000000000000000, %U A135656 111111111111111111100000000000000000,111111111111111111111111111111100000000000000000000000000000 %N A135656 Perfect numbers divided by 2, written in base 2. %C A135656 The number of divisors of a(n) is equal to the number of its digits. This number is equal to 2*A000043(n)-2. The number of divisors of a(n) that are powers of 2 is equal to the number of divisors that are multiples of n-th Mersenne prime A000668(n) and this number of divisors is equal to A090748(n). The first digits of a(n) are "1". For n>1 the last digits are "0". The number of digits "1" is equal to A000043(n). The number of digits "0" is equal to A000043(n)-2. The concatenation of digits "1" gives the n-th Mersenne prime written in binary (see A117293(n)). The structure of divisors of a(n) represent a triangle (see example). %H A135656 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>. %F A135656 a(n)=A133028(n) written in base 2. %e A135656 a(4)=111111100000 because the 4th. perfect number is 8128 and 8128/2=4064 and 4064 written in base 2 is 111111100000. Note that 1111111 is the 4th. Mersenne prime A000668(4)=127, written in base 2. %e A135656 The structure of divisors of a(4)=111111100000 %Y A135656 Perfect numbers divided by 2: A133028. Cf. A000396, A000668, A019279, A090748, A117293, A135650. %K A135656 base,nonn,less %O A135656 1,1 %A A135656 _Omar E. Pol_, Feb 28 2008