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Search: id:A033289
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| A033289 |
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Odd Power Perfect numbers: opsigma(n) = 2*n. |
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+0
1
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| 6, 264, 45408, 10177920, 9310826880, 27806077440, 25437179036160, 303753589954560, 277875743791011840, 14504815632384, 13269098919960576, 2534919599177957376, 2318960803647990104064
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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.
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FORMULA
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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.
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EXAMPLE
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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))
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CROSSREFS
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Sequence in context: A053944 A015020 A003384 this_sequence A163015 A049679 A128792
Adjacent sequences: A033286 A033287 A033288 this_sequence A033290 A033291 A033292
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KEYWORD
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nonn
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AUTHOR
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Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp)
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