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A223610
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Numbers k whose abundance is 18: sigma(k) - 2*k = 18.
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3
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208, 6976, 8415, 31815, 351351, 2077696, 20487159, 159030135, 536559616, 2586415095, 137433972736, 2199003332608
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OFFSET
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1,1
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COMMENTS
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a(12) > 10^12.
Any term x of this sequence can be combined with any term y of A223608 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
a(13) <= 2305842988812599296. Every number of the form 2^(j-1)*(2^j - 19), where 2^j - 19 is prime, is a term. - Jon E. Schoenfield, Jun 02 2019
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LINKS
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EXAMPLE
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For k = 159030135, sigma(k) - 2*k = 18.
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MATHEMATICA
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Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == 18 &] (* Vincenzo Librandi, Sep 14 2016 *)
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PROG
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(PARI) for(n=1, 10^8, if(sigma(n)-2*n==18, print1(n ", ")))
(Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq 18]; // Vincenzo Librandi, Sep 14 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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EXTENSIONS
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STATUS
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approved
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