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A280196 Numbers n such that a^(n-1) == 1 (mod n^2) has no solutions with 1 < a < n^2-1.

%I A280196 #9 Apr 27 2019 05:22:12
%S A280196 1,2,3,4,6,8,9,10,12,14,16,18,20,22,24,26,27,30,32,34,36,38,40,42,44,
%T A280196 46,48,50,54,56,58,60,62,64,68,72,74,78,80,81,82,84,86,88,90,92,94,96,
%U A280196 98,100,102,104,106,108,110,114,116,118,120,122,126,128,132,134,136,138
%N A280196 Numbers n such that a^(n-1) == 1 (mod n^2) has no solutions with 1 < a < n^2-1.
%C A280196 1 and numbers n such that A185103(n) = n^2 + (-1)^n.
%C A280196 Complement of A280199.
%C A280196 Union of A000244 and A209211.
%H A280196 Robert Israel, <a href="/A280196/b280196.txt">Table of n, a(n) for n = 1..10000</a>
%e A280196 a(4) = 4 is in the sequence because a^3 == 1 (mod 4^2) has no solutions except a == 1 (mod 4^2).
%e A280196 a(7) = 9 is in the sequence because a^8 == 1 (mod 9^2) has no solutions except a == 1 (mod 9^2) and a == 80 (mod 9^2), and 80 = 9^2-1.
%p A280196 Aeven:= select(t -> igcd(t-1, numtheory:-phi(t^2))=1, {seq(i,i=2..1000,2}}):
%p A280196 Aodd:= {seq(3^i,i=0..floor(log[3](1000)))}:
%p A280196 sort(convert(Aeven union Aodd, list));
%t A280196 Aeven = Select[Range[2, 1000, 2], GCD[#-1,EulerPhi[#^2]] == 1&];
%t A280196 Aodd = 3^Range[0, Floor[Log[3, 1000]]];
%t A280196 Union[Aeven, Aodd] (* _Jean-François Alcover_, Apr 27 2019, from Maple *)
%Y A280196 Cf. A000244, A185103, A209211, A280199.
%K A280196 nonn
%O A280196 1,2
%A A280196 _Robert Israel_ and _Thomas Ordowski_, Dec 28 2016