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 A001115 Maximal number of pairwise relatively prime polynomials of degree n over GF(2). (Formerly M0575 N0209) 1
 1, 2, 3, 4, 6, 9, 14, 23, 38, 64, 113, 200, 358, 653, 1202, 2223, 4151, 7781, 14659, 27721, 52603, 100084, 190969, 365134, 699617, 1342923, 2582172, 4972385, 9588933, 18515328, 35794987, 69278386, 134224480, 260309786, 505302925, 981723316, 1908898002, 3714597352, 7233673969, 14096361346, 27487875487 (list; graph; refs; listen; history; text; internal format)
 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 Bossen, D. C. and Yau, S. S.; Redundant residue polynomial codes. Information and Control 13 (1968) 597-618. 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 FORMULA a(n) = P(n) + sum_{i from 1 to 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=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 (PARI) A001115(n)=A001037(n)+sum(i=1, n\2, A001037(i)) \\ M. F. Hasler, Jan 11 2016 CROSSREFS Sequence in context: A256969 A005579 A000381 * A173278 A173289 A096824 Adjacent sequences:  A001112 A001113 A001114 * A001116 A001117 A001118 KEYWORD nonn AUTHOR EXTENSIONS Edited by Dean Hickerson, Nov 18 2002 More terms from M. F. Hasler, Jan 11 2016 STATUS approved

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Last modified August 10 04:38 EDT 2020. Contains 336368 sequences. (Running on oeis4.)