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<DIV><FONT color=#000000 size=2> Hi Farideh</FONT></DIV>
<DIV><FONT color=#000000 size=2></FONT><FONT size=2></FONT> </DIV>
<DIV><FONT size=2> Thanks for your searching NPPS perfect
number.</FONT></DIV>
<DIV><FONT size=2> It is nice that the number of terms
becomes more than four.</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2> Yasutoshi</FONT></DIV>
<DIV><FONT size=2></FONT>
<DIV> </DIV>
<DIV> >It is intersting that the next NPPS perfect number
is </DIV>
<DIV> >least common multiple of 13770 & 111552
,i.e.</DIV>
<DIV> >a(5)=lcm(13770,111552)=256011840.</DIV>
<DIV> </DIV>
<DIV><FONT color=#000000 size=2> Yes, it is. I didn't
expect such a example. </FONT></DIV>
<DIV> </DIV></DIV>
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style="BORDER-LEFT: #000000 solid 2px; MARGIN-LEFT: 5px; PADDING-LEFT: 5px">
<DIV><FONT face="ＭＳ Ｐゴシック" size=2><BR> </DIV></FONT>
<DIV>Hi Yasutoshi,</DIV>
<DIV> </DIV>
<DIV>According to your definition of " NPPS perfect number " 13770
is <BR>a NPPS perfect number because, </DIV>
<DIV> </DIV>
<DIV>13770=2*3^4*5*17 so,</DIV>
<DIV> </DIV>
<DIV>NPPSigma(2*3^4*5*17)=(1+2^1)*(1+3^1+3^4)*(1+5^1)*(1+17^1)=2*13770.</DIV>
<DIV> </DIV>
<DIV>In fact all NPPS perfect numbers up to 10^8 are 6,4560,13770 &
111552.</DIV>
<DIV><BR>Farideh </DIV>
<DIV><BR><BR>Quoting "y.kohmoto" <<A
href="mailto:zbi74583@boat.zero.ad.jp">zbi74583@boat.zero.ad.jp</A>>:</DIV>
<DIV>> To Neil :<BR>>
I post a sequence of NPPS perfect number.<BR>>
<BR>> %I A000001<BR>>
%S A000001 6, 4560, 111552<BR>> %N A000001
Non Prime Power Sigma perfect
number.<BR>>
NPPSigma(n)=2*n<BR>>
Here, if n=Product p_i^r_i then<BR>> NPPSigma(n)=Product{Sum p_i^s_i, s_i
is not a prime number, 0<=s_i<=r_i}<BR>> %e
A000001
NPPSigma(2^5*7^4)=(1+2+2^4)*(1+7+7^4)=45771<BR>>
All powers of the terms are not
primes.<BR>>
Factorizations : 2*3, 2^4*3*5*19, 2^6*3*7*83,<BR>>
<BR>> %Y A000001
A096290<BR>> %K A000001
nonn<BR>> %O A000001 1,
1<BR>> %A A000001 Yasutoshi Kohmoto (<A
href="mailto:zbi74583@boat.zero.ad.jp">zbi74583@boat.zero.ad.jp</A>)<BR>>
<BR>> I calculated the solutions whose power of
factor 2 is up to 16, only<BR>> three examples
exist.<BR>> Isn't it fit to OEIS which needs four
terms?<BR>> <BR>> If not, I will describe it
on my OEUAI.<BR>> <BR>> Yasutoshi<BR></DIV>
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