Non prime power sigma

Tue Nov 9 04:17:50 CET 2004

```    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

>     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

----------------------------------------------------------------------------
Yahoo! Messenger - Communicate instantly..."Ping" your friends today!