PPsigma

[y.kohmoto]

    Neil.
    I post a sequence related with PPSigma function.



%I A0000001
%S A000001 216, 1149984, 365727111552, 1590733122516339863159808000
%N A000001 Prime power perfect number :
                    If n=Product p_i^r_i
                    then PPsigma(n)= Product {Sum p_i^s_i , 2<=s_i<=r_i ,
s_i is prime}
                    PPsigma(n)=2*n
%e A000001 PPsigma(2^5*3^3)=(2^2+2^3+2^5)*(3^2+3^3)=1584
                    All powers of the terms are prime.
%C A000001 Factorizations :
                    2^3*3^3, 2^5*3^3*11^3, 2^7*3^3*11^3*43^3,
2^13*3^5*5^3*19^3*23^3*31^3*137^3
                    No square free solution exists. All primes are cubic at
least.
%K A000001 nonn
 %O A000001 1, 1
 %A A000001 Yasutoshi Kohmoto (zbi74583 at boat.zero.ad.jp)



    Yasutoshi