names of fuctions

[y.kohmoto]

    Hello, seqfans
    I wonder if the following functions have their names.

    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

    Anyone who knows their names, please tell me them.
    If we use these functions, the definition of  K-sequence becomes much
easier.
    a(n)=g_p ([A*a(n-1)+B])

    Yasutoshi
    http://boat.zero.ad.jp/~zbi74583/another02.htm