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 A054717 #16 Aug 25 2024 10:00:50
%S A054717 1,1,2,1,2,2,3,1,2,2,5,2,3,3,3,2,8,2,9,2,4,5,11,2,10,3,3,3,14,3,15,4,
%T A054717 6,8,6,2,9,9,4,2,4,4,21,5,3,11,23,3,21,10,9,3,26,3,10,3,10,14,29,3,5,
%U A054717 15,4,8,6,6,11,8,12,6,35,2,6,9,11,9,15,4,39,2,3,4,41,4,8,21,15,5,44,3,3
%N A054717 Number of powers of 9 modulo n.
%H A054717 Amiram Eldar, <a href="/A054717/b054717.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from David W. Wilson)
%F A054717 a(n) = valuation(3*n, 9) + A007740(n). - _Amiram Eldar_, Aug 25 2024
%e A054717 Take the sequence 1, 9, 81, 729, ... and reduce mod n; count distinct terms. For n = 5 we get 1, 4, 1, 4, ... so a(5) = 2.
%t A054717 With[{p9=9^Range[0,50]},Table[Length[Union[Mod[#,n]&/@p9]],{n,100}]] (* _Harvey P. Dale_, Apr 22 2012 *)
%t A054717 a[n_] := IntegerExponent[3*n, 9] + MultiplicativeOrder[9, n/3^IntegerExponent[n, 3]]; Array[a, 100] (* _Amiram Eldar_, Aug 25 2024 *)
%Y A054717 Cf. A007740.
%Y A054717 Cf. A054703 (base 2), A054704 (3), A054705 (4), A054706 (5), A054707 (6), A054708 (7), A054709 (8), A054710 (10), A351524 (11), A054712 (12), A054713 (13), A054714 (14), A054715 (15), A054716 (16).
%K A054717 easy,nonn
%O A054717 1,3
%A A054717 _Henry Bottomley_, Apr 20 2000