names of functions

[y.kohmoto]

    Hello, Don McDonald
    Thanks for your answer, but sometimes I don't understand well the reason
of your additional message for my questions.
    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
    http://boat.zero.ad.jp/~zbi74583/another02.htm