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Number of powers of 8 modulo n.
15

%I #13 Aug 25 2024 10:00:22

%S 1,2,2,2,4,3,1,2,2,5,10,3,4,2,4,3,8,3,6,5,2,11,11,3,20,5,6,2,28,5,5,3,

%T 10,9,4,3,12,7,4,5,20,3,14,11,4,12,23,4,7,21,8,5,52,7,20,2,6,29,58,5,

%U 20,6,2,3,4,11,22,9,22,5,35,3,3,13,20,7,10,5,13,6,18,21,82,3,8,15,28

%N Number of powers of 8 modulo n.

%H Amiram Eldar, <a href="/A054709/b054709.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from David W. Wilson)

%F a(n) = valuation(4*n, 8) + A007739(n). - _Amiram Eldar_, Aug 25 2024

%t a[n_] := IntegerExponent[4*n, 8] + MultiplicativeOrder[8, n/2^IntegerExponent[n, 2]]; Array[a, 100] (* _Amiram Eldar_, Aug 25 2024 *)

%Y Cf. A007739.

%Y Cf. A054703 (base 2), A054704 (3), A054705 (4), A054706 (5), A054707 (6), A054708 (7), 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