quiz

[y.kohmoto]

    JEREMY GARDINER wrote :
    >Looks like A048645 (Integers with one or two 1-bits in their binary
expansion) but then what's the connection with A092760?

    >"y.kohmoto" <zbi74583 at boat.zero.ad.jp> wrote:
    >>What is this sequence?
    >>1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 20, 24, ....
    >>Hint :
    >>It is a generalization of A092760, but it became an absolutely
different sequence.



    Really? It is  interesting.
    The definition of this sequence :
    USUP(USUP(n))=1/k*n, for some integer k.
              If n=Product p_i^r_i then
              USUP(n)=UnitarySigma(2^r_1)*UnitaryPhi(n/2^r_1)
              =(2^r_1+1)*Product(p_i^r_i-1) , 2<p_i.

    And A092760 :
    USUP(n)=1/k*n, for some integer k.
              If n=Product p_i^r_i then
              USUP(n)=UnitarySigma(2^r_1)*UnitaryPhi(n/2^r_1)
              =(2^r_1+1)*Product(p_i^r_i-1) , 2<p_i.



    I am able to suppose a part of reason why it looks like A048645, but it
might be a accident.
    Does someone know the probability that first  fifteen terms of two
sequences are same?

    >USUP
    1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 20, 24, 34, 36, 40, 48, 68,
72, 80,

    >A048645
    1,2,3,4,5,6,8,9,10,12,16,17,18,20,24,32,33,34,36,40,48,64,65,66,68,72

    Yasutoshi