Non prime power sigma

[y.kohmoto]

    Hi Farideh

    Thanks for your searching NPPS perfect number.
    It  is nice that the number of terms becomes more than four.

    Yasutoshi

    >It is intersting that the next NPPS perfect number is
    >least common multiple of 13770 & 111552 ,i.e.
    >a(5)=lcm(13770,111552)=256011840.

    Yes, it is. I didn't expect   such a example.



    Hi Yasutoshi,

    According to your definition of " NPPS perfect number " 13770 is
    a NPPS perfect number because,

    13770=2*3^4*5*17  so,

    NPPSigma(2*3^4*5*17)=(1+2^1)*(1+3^1+3^4)*(1+5^1)*(1+17^1)=2*13770.

    In fact all NPPS perfect numbers up to 10^8 are 6,4560,13770 & 111552.

    Farideh


    Quoting "y.kohmoto" <zbi74583 at boat.zero.ad.jp>:
    >     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.
    >                       NPPSigma(n)=2*n
    >                       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 boat.zero.ad.jp)
    >
    >     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.
    >
    >     Yasutoshi



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