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Number of powers of 6 modulo n.
15

%I #13 Aug 25 2024 09:59:29

%S 1,2,2,3,1,2,2,4,3,2,10,3,12,3,2,5,16,3,9,3,3,11,11,4,5,13,4,4,14,2,6,

%T 6,11,17,2,3,4,10,13,4,40,3,3,12,3,12,23,5,14,6,17,14,26,4,10,5,10,15,

%U 58,3,60,7,4,7,12,11,33,18,12,3,35,4,36,5,6,11,10,13,78,5,5,41,82,4,16

%N Number of powers of 6 modulo n.

%H Amiram Eldar, <a href="/A054707/b054707.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from David W. Wilson)

%F a(n) = A007737(n) + A244417(n). - _Amiram Eldar_, Aug 25 2024

%t a[n_] := Module[{e = IntegerExponent[n, {2, 3}]}, Max[e] + MultiplicativeOrder[6, n/Times @@ ({2, 3}^e)]]; Array[a, 100] (* _Amiram Eldar_, Aug 25 2024 *)

%Y Cf. A007737, A244417.

%Y Cf. A054703 (base 2), A054704 (3), A054705 (4), A054706 (5), 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