%I #32 Feb 17 2022 00:01:23

%S 1,2,9,16,625,36,117649,4096,531441,10000,25937424601,20736,

%T 23298085122481,7529536,2562890625,4294967296,48661191875666868481,

%U 34012224,104127350297911241532841,25600000000,7355827511386641

%N a(n) = n^phi(n).

%H T. D. Noe, <a href="/A062981/b062981.txt">Table of n, a(n) for n = 1..100</a>

%H Brett A. Harrison, <a href="http://www.jstor.org/stable/27642336">On the reducibility of cyclotomic polynomials over finite fields</a>, Am. Math. Monthly, Vol. 114, No. 9 (2007), pp. 813-818.

%F a(n) = A001783(n) / (Product_{d|n} (d!/d^d)^A008683(n/d)) = (Product_{GCD(k, n)=1} k) / (Product_{d|n} (d!/d^d)^A008683(n/d)) = A175504(n) * n. - _Jaroslav Krizek_, May 31 2010

%F Sum_{n>=1} 1/a(n) = A239725. - _Amiram Eldar_, Nov 19 2020

%p A062981 := proc(n)

%p n^numtheory[phi](n) ;

%p end proc:

%p seq(A062981(n),n=1..20) ; # _R. J. Mathar_, Oct 15 2011

%t Table[n^EulerPhi[n],{n,30}] (* _Harvey P. Dale_, Mar 30 2012 *)

%o (PARI) a(n) = n^eulerphi(n); \\ _Harry J. Smith_, Aug 14 2009

%o (Magma) [n^EulerPhi(n): n in [1..25]]; // _Vincenzo Librandi_, Apr 05 2017

%Y Cf. A000010, A004124, A193679, A239725.

%K nice,nonn

%O 1,2

%A _Reinhard Zumkeller_, Jul 24 2001