multiplicative

[kohmoto]

    Neil

    I post a multiplicative sequence.

    %I A000001
    %S A000001 1, 3, 2, 5, 4, 6, 6, 9, 8, 12, 10, 10, 12, 18, 8, 17, 16, 24, 
18, 20,
    %N A000001 UnitarySigmaUnitaryPhi(n) or USUP(n)
    %C A000001 USUP(n) is defined  as follows.
                     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.

                      So USUP(n) = UnitarySigma(n) if n=2^r
                                       = UnitaryPhi(n) if GCD(2,n)=1

    %e A000001  USUP(2^4*7^2)=UnitarySigma(2^4)*UnitaryPhi(7^2)=17*48= 816

    %Y A000001 A093760
    %K A000001 none, mult
    %O A000001 1,2
    %A A000001 Yasutsohi Kohmoto    (zbi74583 at boat.zero.ad.jp).
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