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I want to do prime factorization of following $a$

a=sqrt(2)+6-sqrt(2)
a.factor()

But sage says simply

6

What should I do?

(I originally wanted to factor (((3+sqrt(8))^(1i) +(3-sqrt(8))^(1i))/2) for i in [1..40])

I want to do prime factorization of following $a$

a=sqrt(2)+6-sqrt(2)
a.factor()

But sage says simply

6

What should I do?

(I originally wanted to factor (((3+sqrt(8))^(1i) +(3-sqrt(8))^(1i))/2) $((3+\sqrt{8})^i +(3-\sqrt{8})^i)/2$ for i in [1..40])

I want to do prime factorization of following $a$

a=sqrt(2)+6-sqrt(2)
a.factor()

But sage says simply

6

What should I do?

(I originally wanted to factor $((3+\sqrt{8})^i +(3-\sqrt{8})^i)/2$ $\frac{(3+\sqrt{8})^i +(3-\sqrt{8})^i}{2}$ for i in [1..40])