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

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, 46, 48, 50, 54, 56, 58, 60, 62, 64, 68, 72, 74, 78, 80, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 114, 116, 118, 120, 122, 126, 128, 132, 134, 136, 138

Offset: 1

Author

Robert Israel and Thomas Ordowski, Dec 28 2016

Keywords

• nonn

Comments

1 and numbers n such that A185103(n) = n^2 + (-1)^n.

Complement of A280199.

Union of A000244 and A209211.

Examples

			a(4) = 4 is in the sequence because a^3 == 1 (mod 4^2) has no solutions except a == 1 (mod 4^2).
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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000244, A185103, A209211, A280199.

Programs

Maple

Aeven:= select(t -> igcd(t-1, numtheory:-phi(t^2))=1, {seq(i,i=2..1000,2}}):
Aodd:= {seq(3^i,i=0..floor(log[3](1000)))}:
sort(convert(Aeven union Aodd, list));

Mathematica

Aeven = Select[Range[2, 1000, 2], GCD[#-1,EulerPhi[#^2]] == 1&];
Aodd = 3^Range[0, Floor[Log[3, 1000]]];
Union[Aeven, Aodd] (* Jean-François Alcover, Apr 27 2019, from Maple *)