two divisor sequences

[kohmoto]

    Neil
    I submit two Sigma sequences.



    %I A000001
    %S A000001 1, 2, 2, 4, 3, 4, 3, 6, 5, 6, 4, 8
    %N A000001 SquareRootSigma(n) : Integerization of sum of square root of 
divisors of n
                     If n = Product p_i^r_i then SRSigma(n) = Product 
Floor[(p_i^(r_i/2+1/2)-1)/(p_i^(1/2)-1) ].　
    %O A000001     1.2
    %Y A000001    A033635
    %K A000001    nonn, mult
    %A A000001    Yasutoshi Kohmoto (zbi74583 at boat.zero.ad.jp)



    %I A000002
    %S A000002 1, 1, 2, 5, 4, 2, 6, 13, 11, 4, 10, 10, 12, 6, 8, 29, 16, 11, 
19, 20
    %N A000002 (-1)Sigma(n) : a difference of divisors of n
                     If x=Product p_i^r_i, then (-1)Sigma(x)=Product (-1+Sum 
p_i^s_i, s_i=1 to r_i) = Product ((p_i^(r_i+1)-1)/(p_i-1)-2)
                     (-1)Sigma(1)=1
　　%e A000002
　　　　            (-1)sigma(24)=(-1+2+4+8)*(-1+3)=1-2-4-8-3+6+12+24
　　　　            all terms are divisors of 24, but it is not the sum of 
divisors.
　　　　            It is a difference of divisors.
    %O A000002     1.3
    %Y A000002    A0
    %K A000002    nonn, mult
    %A A000002    Yasutoshi Kohmoto (zbi74583 at boat.zero.ad.jp)



    Yasutsohi
 
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