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.
Divisors[10^15-1] (* Harvey P. Dale, Jul 22 2014 *)
{ divisors(10^15-1) } \\ Harry J. Smith, Mar 08 2009
Divisors[10^16-1] (* Harvey P. Dale, Aug 30 2014 *)
divisors(10^16-1) \\ Charles R Greathouse IV, Jun 21 2017
Divisors[10^18 - 1][[;;100]] (* Paolo Xausa, Jul 31 2024 *)
divisors(10^18-1) \\ Charles R Greathouse IV, Jun 21 2017
Divisors[10^17-1] (* Harvey P. Dale, Jan 20 2013 *)
divisors(10^17-1) \\ Charles R Greathouse IV, Jun 21 2017
3 and 9 qualify for the first 2 terms because both of them have a reciprocal cycle of 1. Then 11 has a reciprocal cycle of 2; then 27 and 37 have 3; then 101 has 4; then 41 and 271 have 5. Table begins: 3, 9; 11; 27, 37; 101; 41, 271; 7, 13; 239, 4649; 73, 137; 81, 333667; 9091; 21649, 513239; 9901; 53, 79, 265371653;
go(n)=my(v=[],P=[],E=[],t,ok); for(k=1,n, t=setminus(factor(10^k-1)[,1]~,P); E=concat(E,vector(#t,i,1)); P=concat(P,t); E=apply(i->E[i],Vec(vecsort(P,,1))); P=vecsort(P); ok=1; while(ok, ok=0; for(i=1,#P,if(znorder(Mod(10,P[i]^(E[i]+1)))==k, E[i]++; t=concat(t,P[i]^E[i]); ok=1))); v=concat(v,t=vecsort(t)); print(k" "t)); v \\ Charles R Greathouse IV, Aug 01 2013