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 A327836 #25 Feb 02 2025 04:28:18
%S A327836 1,18,64,1250,3888,235298,2097152,86093442,250000000,51874849202,
%T A327836 743008370688,46596170244962,396857386627072,58385852050781250,
%U A327836 1152921504606846976,97322383751333736962,273238944967337066496,208254700595822483065682,5242880000000000000000000,556436858893903097274392802
%N A327836 Least k > 0 such that n^k == 1 (mod (n+1)^(n+1)).
%C A327836 Alternative description: For each n, a(n) gives the first k such that n^k-1 has (n+1)^(n+1) as a factor.
%C A327836 As n^(m*k)-1 = (n^k)^m-1 is divisible by n^k-1 for all m >= 1, all integer multiples k = m*a(n), m >= 1, also give n^k == 1 (mod (n+1)^(n+1)).
%C A327836 Conjecture: a(n) <= 2*(n+1)^n.
%e A327836 For n=2: 2^18-1 has the factor 27=3^3.
%e A327836 For n=3: 3^64-1 has the factor 256=2^8=4^4.
%p A327836 a:= n-> (t-> numtheory[order](n, t^t))(n+1):
%p A327836 seq(a(n), n=1..20); # _Alois P. Heinz_, Sep 27 2019
%t A327836 a[n_] := MultiplicativeOrder[n, (n+1)^(n+1)];
%t A327836 Table[a[n], {n, 1, 19}] (* _Jean-François Alcover_, Feb 02 2025, after PARI code *)
%o A327836 (PARI) a(n) = znorder(Mod(n, (n+1)^(n+1))); \\ _Daniel Suteu_, Sep 27 2019
%K A327836 nonn
%O A327836 1,2
%A A327836 _Matthias Baur_, Sep 27 2019
%E A327836 More terms from _Daniel Suteu_, Sep 27 2019