%I #15 Aug 25 2024 09:58:53
%S 1,2,1,2,2,2,3,3,3,3,5,2,6,4,2,3,4,4,9,3,3,6,11,3,10,7,9,4,14,3,5,4,5,
%T 5,6,4,18,10,6,4,10,4,7,6,6,12,23,3,21,11,4,7,26,10,10,5,9,15,29,3,30,
%U 6,3,4,6,6,33,5,11,7,35,5,9,19,10,10,15,7,39,4,27,11,41,4,4,8,14,7,11
%N Number of powers of 4 modulo n.
%H Amiram Eldar, <a href="/A054705/b054705.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from David W. Wilson)
%F a(n) = A007735(n) + A244415(n). - _Amiram Eldar_, Aug 25 2024
%t a[n_] := IntegerExponent[2*n, 4] + MultiplicativeOrder[4, n/2^IntegerExponent[n, 2]]; Array[a, 100] (* _Amiram Eldar_, Aug 25 2024 *)
%Y Cf. A007735, A244415.
%Y Cf. A054703 (base 2), A054704 (3), 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