Search: id:A033289
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%I A033289
%S A033289 6,264,45408,10177920,9310826880,27806077440,25437179036160,
%T A033289 303753589954560,277875743791011840,14504815632384,
%U A033289 13269098919960576,2534919599177957376,2318960803647990104064
%N A033289 Odd Power Perfect numbers: opsigma(n) = 2*n.
%C A033289 If x is OPP and x=2^k*y, gcd(2^k,y)=1, (2^(k+4)+1)/3 is prime, then 4*x*(2^(k+4)+1)/
               3 is also OPP.
%F A033289 If n = Product p(i)^r(i) then opsigma(n) = Product (1+(p(i)^(s(i)+2)-p(i))/
               (p(i)^2-1)) where s(i)=r(i) if r(i) is odd, s(i)=r(i)-1 if r(i) is 
               even.
%e A033289 If n=p1^r1*p2^r2*p3^r3*... then opsigma(n)=(1+p1+p1^3+p1^5+ ... +p1^r1)*(1+p2+p2^3+p2^5+ 
               ... +p2^r2)*(1+p3+p3^3+p3^5+ ... +p3^r3)*... except if ri is even 
               then use (1+pi+pi^3+pi^5+ ... +pi^(ri-1))
%Y A033289 Sequence in context: A053944 A015020 A003384 this_sequence A163015 A049679 
               A128792
%Y A033289 Adjacent sequences: A033286 A033287 A033288 this_sequence A033290 A033291 
               A033292
%K A033289 nonn
%O A033289 0,1
%A A033289 Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp)

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