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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
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..102.

A. Karttunen, Scheme-program for computing this sequence.

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A182134 A189684 A308176 * A309981 A083338 A241900

Adjacent sequences:  A106490 A106491 A106492 * A106494 A106495 A106496

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 09 2005

STATUS

approved

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)