%I #23 Aug 25 2024 09:58:46
%S 1,2,2,3,4,3,3,4,6,5,10,4,12,4,4,5,8,7,18,6,6,11,11,5,20,13,18,5,28,5,
%T 5,6,10,9,12,8,36,19,12,7,20,7,14,12,12,12,23,6,21,21,8,14,52,19,20,6,
%U 18,29,58,6,60,6,6,7,12,11,66,10,22,13,35,9,9,37,20,20,30,13,39,8,54
%N Number of distinct powers of 2 modulo n.
%H Alois P. Heinz, <a href="/A054703/b054703.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%F a(n) = A007814(n) + A007733(n). - _Max Alekseyev_, May 13 2016
%t a[n_] := Module[{e = IntegerExponent[n, 2]}, e + MultiplicativeOrder[2, n/2^e]]; Array[a, 100] (* _Amiram Eldar_, Aug 25 2024 *)
%Y Cf. A007733, A007814.
%Y Cf. A054704 (base 3), A054705 (4), A054706 (5), A054707 (6), A054708 (7), A054709 (8), A054717 (9), A054710 (10), A351524 (11), A054712 (12), A054713 (13), A054714 (14), A054715 (15), A054716 (16).
%K easy,nonn
%O 1,2
%A _Henry Bottomley_, Apr 20 2000
%E Definition improved by _T. D. Noe_, Jul 21 2008