more divisor sequences

[kohmoto]

    Neil
    I submitt two Sigma sequences.


     %I A000001
    %S A000001 1, 4, 5, 8, 7, 20, 9, 16, 14, 28, 13, 40, 15, 36, 35, 32, 19, 
56, 21, 56
    %N A000001  (+2)Sigma(n) : If n=Product p_i^r_i  then 
(+2)Sigma(n)=Product (2+Sum p_i^s_i, s_i=1 to 
r_i)=Product(1+(p_i^(r_i+1)-1)/(p_i-1)) ,
                      (+2)Sigma(1)=1
    %e A000001               (+2)Sigma(6)=(2+2)*(2+3)=20.
    %O A000001     1,2
    %Y A000001    A000002, A052396
    %K A000001    nonn, mult,
    %A A000001    Yasutoshi Kohmoto (zbi74583 at boat.zero.ad.jp)

    %I A000002
    %S A000002 1, 4, 5, 6, 7, 20, 9, 10, 11, 28, 13, 30, 15, 36, 35, 18, 19, 
44, 21, 42
    %N A000002  (+2)UnitarySigma(n) : If n=Product p_i^r_i  then 
(+2)Sigma(n)=Product (2+p_i^r_i) ,
                      (+2)UnitarySigma(1)=1
    %e A000001               (+2)UnitarySigma(12)=(2+3)*(2+4)=30.
    %O A000001     1,2
    %Y A000001    A000001, A054862
    %K A000001    nonn, mult,
    %A A000001    Yasutoshi Kohmoto (zbi74583 at boat.zero.ad.jp)

    Yasutoshi
 
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