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

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

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: A189684 A308176 A354257 * A309981 A083338 A241900

Adjacent sequences: A106490 A106491 A106492 * A106494 A106495 A106496

Keyword

nonn

Author

Antti Karttunen, May 09 2005

Status

approved