# names of functions

Sat Apr 19 05:05:25 CEST 2003

```    Hello, Don McDonald
Thanks for your answer, but sometimes I don't understand well the reason
What is a relationship between the questions and your sequence?

>What is K-sequence, perhaps kohmoto?
Here is an example of K-sequence at the end of this mail.

to seqfans :
No one told me the names of functions:
>a function which chooses p power in the factorization of n :
>n=product p_i^r_i    ->    f_p (n)=p^r , where p=p_i, r=r_i
>ex.    f_3 (720)=f_3 (2^4*3^2*5)=3^2 , f_7 (15)=1

>a function which deletes  p power in the factorization of n :
>n=product p_i^r_i    ->    g_p (n)=n/p^r , where p=p_i, r=r_i
>ex.    g_3 (720)=g_3 (2^4*3^2*5)=2^4*5 , g_7 (15)=15

Does it mean they don't exist?
If so, let's give them names.

fac_p (n) =  p^r,  where p^r is the highest power of p dividing n.
cof_p (n) =  n/p^r,  where p^r is the highest power of p dividing n.

I use this useful  function  for describing a K-sequence.

x(0)=2443499297
x(n) = cof_2 ([2.00014*x(n-1)+3.0])

The 68 terms from 0-th to 67-th are represented as follows.
x(n) = 6*n^2+171040*n+2443499297

It is strange, isn't it?

Yasutoshi