A177012 Numbers k such that k^k == -1 (mod phi(k)).

1, 2, 3, 15, 87, 255, 11759, 26279, 39455, 43919, 65535, 112895, 443807, 1347455, 1464911, 1568255, 1604559, 1968095, 2441559, 5948799, 16210655, 39624767, 39839039, 59187455, 81624279, 83623935, 251009695, 256685439, 338979839, 434357967, 455345855, 471783935, 487722815, 518291135, 596835839

Offset: 1

Author

Farideh Firoozbakht, May 19 2010

Keywords

• nonn

Comments

3 is the largest prime term of this sequence.

All terms are squarefree. There is no further term up to 2*10^8.

If phi(k) divides k+1 then k is in the sequence. This implies A050474 and A203966 are subsequences of this sequence. - Jahangeer Kholdi, Dec 10 2014

Examples

			phi(15)=8 and 15^15 == -1 (mod 8), so 15 is in the sequence.
		

Crossrefs

Cf. A000010, A177006.

Cf. A050474, A203966.

Programs

Mathematica

v={};Do[If[PowerMod[n,n,EulerPhi[n]]==EulerPhi[n]-1,AppendTo[v,n];
Print[v]],{n,200000000}]

Extensions

a(27)-a(29) from Jahangeer Kholdi, Dec 10 2014

a(30)-a(35) from Farideh Firoozbakht, Dec 10 2014