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 A053163 #16 Jun 30 2015 08:57:11
%S A053163 1,4,8,16,32,32,64,128,128,256,512,512,1024,1024,2048,2048,4096,4096,
%T A053163 8192,8192,8192,16384,16384,32768,32768,65536,65536,131072,131072,
%U A053163 131072,262144,262144,524288,524288,524288,524288,1048576,1048576,1048576,2097152
%N A053163 n+cototient(n) produces these powers of 2 in order of magnitude.
%C A053163 See especially A053579 and also A053576, A053577.
%H A053163 Donovan Johnson, <a href="/A053163/b053163.txt">Table of n, a(n) for n = 1..100</a>
%H A053163 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F A053163 a(n) = 2^w = m+A051953(m) = 2*m-A000010(m) for some m.
%e A053163 1+Mersenne primes powers of 2 are here, 2^p for special primes. Also because of other (infinite) subsequences, all 2-powers from 2^6 occurs at least twice.
%t A053163 Join[{1}, Reap[For[n=3, n<10^7, n++, If[PrimeNu[k = 2*n - EulerPhi[n]] == 1, Print[k]; Sow[k]]]][[2, 1]]] (* _Jean-François Alcover_, Jun 30 2015, after _Donovan Johnson_ *)
%o A053163 (PARI) print(1); for(n=3, 10^9, k=2*n-eulerphi(n); if(omega(k)==1, print(k))) /* _Donovan Johnson_, Apr 04 2013 */
%Y A053163 Cf. A000043, A000668, A001348.
%K A053163 nice,nonn
%O A053163 1,2
%A A053163 _Labos Elemer_, Feb 29 2000
%E A053163 More terms from _Olaf Voß_, Feb 25 2008