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A101223
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Numbers m whose deficiency is 10, or: sigma(m) = 2m - 10.
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10
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11, 21, 26, 68, 656, 2336, 8768, 133376, 528896, 34360918016, 35184409837568, 576460757135261696
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OFFSET
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1,1
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COMMENTS
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A subsequence of A274556. a(11) <= b(23) = 35184409837568 ~ 3.5*10^13, since b(k) := 2^(k-1)*(2^k+9) is in this sequence for all k in A057196 (2^k+9 is prime). All known terms except a(2) = 21 are of that form. - M. F. Hasler, Jul 18 2016
Any term x of this sequence can be combined with any term y of A223609 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable. - Timothy L. Tiffin, Sep 13 2016
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LINKS
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EXAMPLE
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The divisors of 68 are {1, 2, 4, 17, 34, 68} and so sigma(68) = 1 + 2 + 4 + 17+ 24 + 68 = 126 = 2*68 - 10; thus, the deficiency of 68 is 10 so 68 is a term of the sequence.
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MATHEMATICA
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Select[ Range[ 85000000], DivisorSigma[1, # ] + 10 == 2# &]
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PROG
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(Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)) eq 2*n-10]; // Vincenzo Librandi, Sep 15 2016
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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Vassil K. Tintschev (tinchev(AT)sunhe.jinr.ru), Dec 15 2004
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EXTENSIONS
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STATUS
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approved
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