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 A354536 #20 Jan 21 2025 13:31:29
%S A354536 1,3,7,31,127,511,8191,131071,524287,2147483647,2305843009213693951,
%T A354536 147573952589676412927,618970019642690137449562111,
%U A354536 162259276829213363391578010288127,170141183460469231731687303715884105727,174224571863520493293247799005065324265471
%N A354536 Numbers k such that 2*k is in A354525.
%C A354536 Numbers k such that for every prime factor p of k we have gpf(2*k+p) = p, gpf = A006530.
%C A354536 Numbers k such that for every prime factor p of k, 2*k+p is p-smooth.
%C A354536 a(17) = 2^521 - 1 is too large to include here. - _Jinyuan Wang_, Jan 21 2025
%F A354536 a(n) = 2^A354531(n) - 1 = A354533(n)/2.
%e A354536 See A354532.
%o A354536 (PARI) lista(nn,{lim=256},{lim_p=1<<32}) = for(n=1, nn, if(isA354531(n,lim,lim_p), print1(2^n-1, ", "))) \\ See A354531 for the function isA354531
%Y A354536 Cf. A006530, A354525, A354531, A354532, A354533, A354537.
%K A354536 nonn,hard
%O A354536 1,2
%A A354536 _Jianing Song_, Aug 17 2022