A177006 Nonprime numbers k such that k^k == 1 (mod phi(k)).

1, 205505, 3499105, 4775905, 6216001, 27371265, 270784801, 477737601, 672819265, 723513345, 1237655809, 1528531585, 1732765105, 2145938433, 2911107585, 3214481761, 3594908865, 3912744705, 3984159201, 4356218881, 4660483521, 5089667905, 5572247601, 5628702769

Offset: 1

Author

Farideh Firoozbakht, May 19 2010

Keywords

• nonn

Comments

For all primes p we have p^p == 1 (mod phi(p)), because p = phi(p) + 1.

All terms are squarefree.

If k is a composite number such that phi(k) divides k-1 then k is in the sequence. What is the first such number? - Jahangeer Kholdi, Dec 10 2014

All terms are odd. - Robert Israel, Dec 12 2014

Examples

			205505 is a nonprime number, phi(205505) = 157168 and 205505^205505 == 1 (mod 157168) so 205505 is in the sequence.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..51

Crossrefs

Cf. A000010, A177012.

Programs

Mathematica

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

PARI

is(n)=Mod(n,eulerphi(n))^n==1 && !isprime(n) \\ Charles R Greathouse IV, Dec 11 2014

Extensions

a(7)-a(8) from Jahangeer Kholdi, Dec 10 2014

a(9)-a(13) from Jahangeer Kholdi, Dec 11 2014

a(14)-a(24) from Giovanni Resta, Apr 28 2017