divisor fanctions

[kohmoto]

    Neil.
    I submitted sequences of Perfect Number using the following divisor 
functions.

    But I think I didn't submitted these divisor functions.
    I suppose OEIS should have them too


    %I A000001
    %S A000001 1, 3, 4, 7, 6, 12, 8, 15, 10, 18, 12, 28, 14, 24, 24, 31, 18, 
30, 20, 42
    %N A000001 OrdinaryUnitarySigma(n) : If n=Product p_i^r_i then 
OUSigma(n)=Sigma(2^r_1)*UnitarySigma(n/2^r_1)=(2^(r_1+1)-1)*Product(p_i^r_i+1), 
p_i is not 2.

    %e A000001 
OUSigma(2^4*7^2)=Sigma(2^4)*UnitarySigma(7^2)=31*50=1550.
    %O A000001     1,2
    %Y A000001    A000002, A091321
    %K A000001    nonn, mult,
    %A A000001    Yasutoshi Kohmoto (zbi74583 at boat.zero.ad.jp)

    %I A000002
    %S A000002 1, 3, 4, 5, 6, 12, 8, 9, 13, 18, 12, 20, 14, 24, 24, 17, 18, 
39, 20, 30
    %N A000002  UnitaryOrdinarySigma(n) : If n=Product p_i^r_i  then 
UOSigma(n)=UnitarySigma(2^r_1)*Sigma(n/2^r_1)=(2^r_1+1)*Product 
(p_i^(r_i+1)-1)/(p_i-1), p_i is not 2.
    %e A000002 
UOsigma(2^4*7^2)=UnitarySigma(2^4)*sigma(7^2)=17*57=969
    %O A000002     1,2
    %Y A000002    A000001, A092356
    %K A000002    nonn, mult,
    %A A000002    Yasutoshi Kohmoto (zbi74583 at boat.zero.ad.jp)

    Yasutoshi

    PS
    Two divisor functions in my May,25 mail don't appear on OEIS.
    Did you see the mail?

    %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 A000002               (+2)UnitarySigma(12)=(2+3)*(2+4)=30.
    %O A000002     1,2
    %Y A000002    A000001, A054862
    %K A000002    nonn, mult,
    %A A000002    Yasutoshi Kohmoto (zbi74583 at boat.zero.ad.jp)




 
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20050611/26e6f584/attachment.htm>