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

1,2

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

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A177012.

Sequence in context: A234836 A206093 A333015 * A236033 A234068 A234069

Adjacent sequences: A177003 A177004 A177005 * A177007 A177008 A177009

Keyword

nonn

Author

Farideh Firoozbakht, May 19 2010

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

Status

approved