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a(n) = |{m : multiplicative order of n mod m = 7}|.
3

%I #14 Jan 26 2025 02:18:22

%S 0,1,2,6,3,2,12,10,12,9,12,6,6,2,8,60,5,6,18,14,42,8,12,14,56,3,12,12,

%T 12,14,8,14,18,12,12,44,27,2,12,4,24,6,40,14,42,6,12,6,150,5,18,60,18,

%U 14,24,4,40,12,60,2,12,6,12,138,49,4,24,2,18,12,40,2

%N a(n) = |{m : multiplicative order of n mod m = 7}|.

%H Alois P. Heinz, <a href="/A218256/b218256.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = tau(n^7-1)-tau(n-1), with tau = A000005.

%p with(numtheory):

%p a:= n-> add(mobius(7/d) *tau(n^d-1), d={1, 7}):

%p seq(a(n), n=1..80);

%t a[n_] := Subtract @@ DivisorSigma[0, {n^7-1, n-1}]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Jan 25 2025 *)

%o (PARI) a(n) = if(n == 1, 0, numdiv(n^7-1) - numdiv(n-1)); \\ _Amiram Eldar_, Jan 25 2025

%Y Row n=7 of A212957.

%Y Cf. A000005, A008683.

%K nonn,changed

%O 1,3

%A _Alois P. Heinz_, Oct 24 2012