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Nontotients of the form 10^k - 2.
0

%I #44 Jul 19 2024 04:35:02

%S 98,998,9998,99998,999998,9999998,99999998,999999998,9999999998,

%T 99999999998,999999999998,9999999999998,99999999999998,

%U 999999999999998,9999999999999998,99999999999999998,999999999999999998,9999999999999999998,99999999999999999998

%N Nontotients of the form 10^k - 2.

%C There are no k for which (2^n)*(5^n)[p1*p2*...*pk]-2[p1*p2*...*pk]=m[(p1-1)*(p2-1)*...*(pk-1)].

%C Up to k = 60, the only totient of the form 10^k-2 is obtained for k=1. - _Giovanni Resta_, Sep 20 2017

%C For 10^k-2 with k > 1 to be a totient, it would have to be of the form (p-1)*p^m for some odd prime p and m >= 2. - _Robert Israel_, Sep 20 2017

%e a(1) = A011557(2) - 2 = A005277(13);

%e a(2) = A011557(3) - 2 = A005277(210);

%e a(3) = A011557(4) - 2 = A005277(2627);

%e a(4) = A011557(5) - 2 = A005277(29747).

%Y Cf. A005277, A011557, A099150.

%K nonn

%O 1,1

%A _Torlach Rush_, Sep 18 2017

%E More terms from _Giovanni Resta_, Sep 20 2017