A177006 - OEIS

%I #24 Feb 11 2021 01:20:40

%S 1,205505,3499105,4775905,6216001,27371265,270784801,477737601,

%T 672819265,723513345,1237655809,1528531585,1732765105,2145938433,

%U 2911107585,3214481761,3594908865,3912744705,3984159201,4356218881,4660483521,5089667905,5572247601,5628702769

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

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

%C All terms are squarefree.

%C 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

%C All terms are odd. - _Robert Israel_, Dec 12 2014

%H Giovanni Resta, <a href="/A177006/b177006.txt">Table of n, a(n) for n = 1..51</a>

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

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

%t Print[v]],{n,200000000}]

%o (PARI) is(n)=Mod(n,eulerphi(n))^n==1 && !isprime(n) \\ _Charles R Greathouse IV_, Dec 11 2014

%Y Cf. A000010, A177012.

%K nonn

%O 1,2

%A _Farideh Firoozbakht_, May 19 2010

%E a(7)-a(8) from _Jahangeer Kholdi_, Dec 10 2014

%E a(9)-a(13) from _Jahangeer Kholdi_, Dec 11 2014

%E a(14)-a(24) from _Giovanni Resta_, Apr 28 2017