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A106493 Total number of bases and exponents in GF(2)[X] Superfactorization of n, excluding the unity-exponents at the tips of branches. 6

%I #6 Mar 31 2012 14:02:21

%S 0,1,1,2,2,2,1,2,2,3,1,3,1,2,2,3,3,3,1,4,2,2,2,3,1,2,3,3,2,3,1,3,2,4,

%T 2,4,1,2,3,4,1,3,2,3,3,3,1,4,2,2,3,3,2,4,1,3,3,3,1,4,1,2,3,3,4,3,1,5,

%U 2,3,2,4,1,2,3,3,2,4,2,5,2,2,3,4,3,3,1,3,2,4,1,4,2,2,3,4,1,3,3,3,3,4

%N Total number of bases and exponents in GF(2)[X] Superfactorization of n, excluding the unity-exponents at the tips of branches.

%C GF(2)[X] Superfactorization proceeds in a manner analogous to normal superfactorization explained in A106490, but using factorization in domain GF(2)[X], instead of normal integer factorization in N.

%H A. Karttunen, <a href="/A091247/a091247.scm.txt">Scheme-program for computing this sequence.</a>

%e a(64) = 3, as 64 = A048723(2,6) = A048723(2,(A048723(2,1) X A048723(3,1))) and there are three non-1 nodes in that superfactorization. Similarly, for 27 = 5x7 = A048723(3,2) X A048273(7,1) we get a(27) = 3. The operation X stands for GF(2)[X] multiplication defined in A048720, while A048723(n,y) raises the n-th GF(2)[X] polynomial to the y:th power.

%Y a(n) = A106490(A106445(n)). a(n) = A106494(n)-A106495(n).

%K nonn

%O 1,4

%A _Antti Karttunen_, May 09 2005

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