OFFSET
1,3
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
Let GF(4) = GF(2)[w], where w^2 + w + 1 = 0. Factorizations of the n-th cyclotomic polynomial over GF(4) for n <= 10:
n = 1: x + 1;
n = 2: x + 1;
n = 3: (x + w)*(x + (w+1));
n = 4: (x + 1)^2;
n = 5: x^4 + x^3 + x^2 + x + 1;
n = 6: (x + w)*(x + (w+1));
n = 7: (x^3 + x + 1)*(x^3 + x^2 + 1);
n = 8: (x + 1)^4;
n = 9: (x^3 + w)*(x^3 + (w+1));
n = 10: x^4 + x^3 + x^2 + x + 1.
MATHEMATICA
a[n_] := EulerPhi[n] / MultiplicativeOrder[4, n / 2^IntegerExponent[n, 2]]; Array[a, 100] (* Amiram Eldar, Jul 21 2024 *)
PROG
(PARI) a(n) = my(s=n/2^valuation(n, 2)); eulerphi(n)/znorder(Mod(4, s))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Sep 26 2019
STATUS
approved