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A218257 a(n) = |{m : multiplicative order of n mod m = 8}|.

%I A218257 #13 Jan 26 2025 02:19:29
%S A218257 0,4,14,8,28,8,48,72,88,36,56,48,112,48,100,16,108,72,228,16,112,96,
%T A218257 128,12,176,72,304,32,112,48,448,144,224,64,84,48,456,144,64,48,528,
%U A218257 48,2064,336,152,48,800,24,300,144,228,96,608,16,704,32,256,96,688
%N A218257 a(n) = |{m : multiplicative order of n mod m = 8}|.
%H A218257 Alois P. Heinz, <a href="/A218257/b218257.txt">Table of n, a(n) for n = 1..10000</a>
%F A218257 a(n) = tau(n^8-1)-tau(n^4-1), with tau = A000005.
%p A218257 with(numtheory):
%p A218257 a:= n-> add(mobius(8/d) *tau(n^d-1), d={4, 8}):
%p A218257 seq(a(n), n=1..80);
%t A218257 a[n_] := Subtract @@ DivisorSigma[0, {n^8-1, n^4-1}]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jan 25 2025 *)
%o A218257 (PARI) a(n) = if(n == 1, 0, numdiv(n^8-1) - numdiv(n^4-1)); \\ _Amiram Eldar_, Jan 25 2025
%Y A218257 Row n=8 of A212957.
%Y A218257 Cf. A000005, A008683.
%K A218257 nonn
%O A218257 1,2
%A A218257 _Alois P. Heinz_, Oct 24 2012