OFFSET
0,2
COMMENTS
For n>=4, a maximal set can be chosen by taking all irreducible polynomials of degree n, the squares of all irreducible polynomials of degree n/2 (if n is even) and, for each irreducible polynomial p of degree d with 1 <= d < n/2, a product p*q where q is irreducible of degree n-d. The q's should all be distinct, which is possible when n>=4.
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
D. C. Bossen and S. S. Yau, Redundant residue polynomial codes, Information and Control 13 (1968) 597-618.
FORMULA
a(n) = P(n) + Sum_{i=1..floor(n/2)} P(i), where P(n) = A001037(n) = number of irreducible polynomials of degree n.
EXAMPLE
n=1: x and x+1.
n=2: x^2, x^2+1, x^2+x+1.
n=3: x^3, x^3+1, x^3+x+1, x^3+x^2+1.
MATHEMATICA
p[0]=1; p[n_] := Sum[If[Mod[n, d]==0, MoebiusMu[n/d]2^d, 0], {d, 1, n}]/n; a[n_] := p[n]+Sum[p[i], {i, 1, Floor[n/2]}]
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by Dean Hickerson, Nov 18 2002
More terms from M. F. Hasler, Jan 11 2016
STATUS
approved