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Number of powers of 3 modulo n.
15

%I #13 Aug 25 2024 09:58:50

%S 1,1,2,2,4,2,6,2,3,4,5,3,3,6,5,4,16,3,18,4,7,5,11,3,20,3,4,6,28,5,30,

%T 8,6,16,12,4,18,18,4,4,8,7,42,10,6,11,23,5,42,20,17,6,52,4,20,6,19,28,

%U 29,5,10,30,8,16,12,6,22,16,12,12,35,4,12,18,21,18,30,4,78,4,5,8,41,7,16

%N Number of powers of 3 modulo n.

%H Alois P. Heinz, <a href="/A054704/b054704.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from David W. Wilson)

%F a(n) = A007734(n) + A007949(n). - _Amiram Eldar_, Aug 25 2024

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

%Y Cf. A007734, A007949.

%Y Cf. A054703 (base 2), 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 1,3

%A _Henry Bottomley_, Apr 20 2000