Non prime power sigma

y.kohmoto zbi74583 at
Sat Nov 6 06:59:44 CET 2004

    To Neil :
    I post a sequence of NPPS perfect number.

    %I A000001
    %S A000001 6, 4560, 111552
    %N A000001  Non Prime Power Sigma perfect number.
                      Here, if n=Product p_i^r_i then
NPPSigma(n)=Product{Sum p_i^s_i, s_i is not a prime number, 0<=s_i<=r_i}
    %e A000001 NPPSigma(2^5*7^4)=(1+2+2^4)*(1+7+7^4)=45771
                     All powers of the terms are not primes.
                     Factorizations : 2*3, 2^4*3*5*19, 2^6*3*7*83,

    %Y A000001 A096290
    %K A000001 nonn
    %O A000001 1, 1
    %A A000001 Yasutoshi Kohmoto (zbi74583 at

    I calculated the solutions whose power of factor 2 is up to 16,    only
three examples exist.
    Isn't it fit to OEIS which needs four terms?

    If not, I will describe it on my OEUAI.


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