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Number of powers of 5 modulo n.
15

%I #13 Aug 25 2024 09:58:59

%S 1,1,2,1,2,2,6,2,6,2,5,2,4,6,3,4,16,6,9,2,6,5,22,2,3,4,18,6,14,3,3,8,

%T 10,16,7,6,36,9,4,3,20,6,42,5,7,22,46,4,42,3,16,4,52,18,6,6,18,14,29,

%U 3,30,3,6,16,5,10,22,16,22,7,5,6,72,36,4,9,30,4,39,5,54,20,82,6,17,42,14

%N Number of powers of 5 modulo n.

%H Alois P. Heinz, <a href="/A054706/b054706.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from David W. Wilson)

%F a(n) = A007736(n) + A112765(n). - _Amiram Eldar_, Aug 25 2024

%t a[n_] := Module[{e = IntegerExponent[n, 5]}, e + MultiplicativeOrder[5, n/5^e]]; Array[a, 100] (* _Amiram Eldar_, Aug 25 2024 *)

%Y Cf. A007736, A112765.

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