Search: id:A001115
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%I A001115 M0575 N0209
%S A001115 1,2,3,4,6,9,14,23,38,64,113,200,358,653,1202,2223,4151,7781,14659,
%T A001115 27721,52603,100084,190969,365134,699617,1342923,2582172,4972385,
%U A001115 9588933,18515328,35794987,69278386,134224480,260309786,505302925
%N A001115 Maximal number of pairwise relatively prime polynomials of degree n over 
               GF(2).
%C A001115 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 A001115 Bossen, D. C. and Yau, S. S.; Redundant residue polynomial codes. Information 
               and Control 13 (1968) 597-618.
%D A001115 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001115 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%F A001115 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 A001115 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 A001115 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]}]
%Y A001115 Sequence in context: A018140 A005579 A000381 this_sequence A096824 A089797 
               A081237
%Y A001115 Adjacent sequences: A001112 A001113 A001114 this_sequence A001116 A001117 
               A001118
%K A001115 nonn
%O A001115 0,2
%A A001115 N. J. A. Sloane (njas(AT)research.att.com).
%E A001115 Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Nov 18 2002

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