A062981 a(n) = n^phi(n).
1, 2, 9, 16, 625, 36, 117649, 4096, 531441, 10000, 25937424601, 20736, 23298085122481, 7529536, 2562890625, 4294967296, 48661191875666868481, 34012224, 104127350297911241532841, 25600000000, 7355827511386641
Offset: 1
Links
- T. D. Noe, Table of n, a(n) for n = 1..100
- Brett A. Harrison, On the reducibility of cyclotomic polynomials over finite fields, Am. Math. Monthly, Vol. 114, No. 9 (2007), pp. 813-818.
Programs
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Magma
[n^EulerPhi(n): n in [1..25]]; // Vincenzo Librandi, Apr 05 2017
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Maple
A062981 := proc(n) n^numtheory[phi](n) ; end proc: seq(A062981(n),n=1..20) ; # R. J. Mathar, Oct 15 2011
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Mathematica
Table[n^EulerPhi[n],{n,30}] (* Harvey P. Dale, Mar 30 2012 *) -
PARI
a(n) = n^eulerphi(n); \\ Harry J. Smith, Aug 14 2009
Formula
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
Sum_{n>=1} 1/a(n) = A239725. - Amiram Eldar, Nov 19 2020