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

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

%S 1,2,2,3,3,4,2,3,4,5,2,5,2,4,3,4,4,6,2,6,3,4,4,5,2,4,5,5,4,5,2,4,4,6,

%T 4,7,2,4,5,6,2,5,4,5,5,6,2,6,4,4,4,5,4,7,2,5,5,6,2,6,2,4,5,5,6,6,2,7,

%U 3,6,4,7,2,4,5,5,4,7,4,7,3,4,6,6,5,6,2,5,4,7,2,7,4,4,5,6,2,6,5,5,6,6

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

%C See comments at A106493.

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

%e a(64) = 5, as 64 = A048723(2,6) = A048723(2,(A048723(2,1) X A048723(3,1))) and there are five nodes in that superfactorization. Similarly, for 27 = 5x7 = A048723(3, A048723(2,1)) X A048273(7,1) we get a(27) = 5. 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) = A106491(A106445(n)). a(n) = A106493(n)+A106495(n).

%K nonn

%O 1,2

%A _Antti Karttunen_, May 09 2005