OFFSET
1,2
COMMENTS
Second row of the array A158502(n, k) = phi(p^k-1)/k, p=prime(n). - R. J. Mathar, Aug 24 2011
From Joerg Arndt, Oct 03 2012: (Start)
Number of base-3, length-n Lyndon words w such that gcd(w, 3^n-1)==1 (where w is interpreted as a radix-3 number); replacing 3 by any prime p gives the analogous statement for GF(p).
The statement above is the consequence of the following.
Let p be a prime and g be a generator of GF(p^n). If w is a base-p, length-n Lyndon word then f=g^w (where w is interpreted as a radix-p number) has an irreducible characteristic polynomial C (over GF(p)) and, if gcd(w,p^n-1)==1 then C is primitive.
(End)
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..200 (terms 1..100 from Seiichi Manyama)
Eric W. Weisstein, MathWorld: Totient Function
Wikipedia, Euler's totient function
MAPLE
A027385 := proc(n) numtheory[phi](3^n-1)/n; end proc:
MATHEMATICA
Table[EulerPhi[3^n - 1]/n, {n, 1, 30}] (* Vaclav Kotesovec, Nov 23 2017 *)
PROG
(PARI) a(n) = eulerphi(3^n-1)/n; /* Joerg Arndt, Aug 25 2011 */
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
STATUS
approved