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Search: id:A091321
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| A091321 |
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OU-Sigma perfect numbers. |
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+0
5
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| 6, 28, 90, 120, 496, 8128, 10080, 63700, 33550336, 8589869056, 22144573440, 51001180160, 153003540480, 243643438080, 583125903360, 71724486113280, 1555825650042470400
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OFFSET
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1,1
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COMMENT
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If n=Product p_i^r_i then we may define the ordinary unitary sigma function by OU-Sigma(n)=Sigma(2^r_1)*UnitarySigma(n/2^r_1) =(2^(r_1+1)-1)*Product(p_i^r_i+1), p_i is not 2.
E.g. OU-Sigma(2^4*7^2)=Sigma(2^4)*UnitarySigma(7^2)=31*50=1550. So OU-Sigma(n) = Sigma(n) if n=2^r = UnitarySigma(n) if GCD(2,n)=1.
Then an OU-Sigma perfect number satisfies OU-Sigma(n) = k*n for some k.
Every perfect number is here because OE-Sigma(2^(m-1)*M_m) = Sigma(2^(m-1))*UnitarySigma(M_m) = Sigma(2^(m-1))*Sigma(M_m) = 2^m*M_m
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EXAMPLE
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Sequence begins 2*3, 2*3^2*5, 2^2*7, 2^2*5^2*7^2*13, 2^3*3*5, 2^4*31, 2^5*3^2*5*7, ...
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CROSSREFS
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Cf. A091322
Sequence in context: A144945 A055711 A141255 this_sequence A125310 A138874 A011856
Adjacent sequences: A091318 A091319 A091320 this_sequence A091322 A091323 A091324
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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), Feb 17 2004
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