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A001115 Maximal number of pairwise relatively prime polynomials of degree n over GF(2).
(Formerly M0575 N0209)
1

%I M0575 N0209

%S 1,2,3,4,6,9,14,23,38,64,113,200,358,653,1202,2223,4151,7781,14659,

%T 27721,52603,100084,190969,365134,699617,1342923,2582172,4972385,

%U 9588933,18515328,35794987,69278386,134224480,260309786,505302925,981723316,1908898002,3714597352,7233673969,14096361346,27487875487

%N Maximal number of pairwise relatively prime polynomials of degree n over GF(2).

%C 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.

%D Bossen, D. C. and Yau, S. S.; Redundant residue polynomial codes. Information and Control 13 (1968) 597-618.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%F 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.

%e 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.

%t 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]}]

%o (PARI) A001115(n)=A001037(n)+sum(i=1,n\2,A001037(i)) \\ _M. F. Hasler_, Jan 11 2016

%K nonn

%O 0,2

%A _N. J. A. Sloane_.

%E Edited by _Dean Hickerson_, Nov 18 2002

%E More terms from _M. F. Hasler_, Jan 11 2016

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Last modified December 12 12:51 EST 2018. Contains 318063 sequences. (Running on oeis4.)