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A141545
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Numbers n whose abundance is 12: sigma(n) - 2n = 12.
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4
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24, 30, 42, 54, 66, 78, 102, 114, 138, 174, 186, 222, 246, 258, 282, 304, 318, 354, 366, 402, 426, 438, 474, 498, 534, 582, 606, 618, 642, 654, 678, 762, 786, 822, 834, 894, 906, 942, 978, 1002, 1038, 1074, 1086, 1146, 1158, 1182, 1194, 1266, 1338, 1362
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OFFSET
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1,1
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COMMENTS
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Numbers k such that sigma(k) = 2k + 12. - Wesley Ivan Hurt, Jul 11 2013
Any term x = a(m) can be combined with any term y = A141549(n) to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2. Although this property is a necessary condition for two numbers to be amicable, it is not a sufficient one. So far, these two sequences have not produced an amicable pair. However, if one is ever found, then it will exhibit y-x = 12. - Timothy L. Tiffin, Sep 13 2016
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LINKS
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Donovan Johnson, Table of n, a(n) for n = 1..10000
F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1
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EXAMPLE
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30 is in the sequence since sigma(30) = sigma(2*3*5) = sigma(2)*sigma(3)*sigma(5) = 3*4*6 = 72 = 2(30)+12. Since this is the second such number whose abundance is 12, a(2) = 30. - Wesley Ivan Hurt, Jul 11 2013
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MATHEMATICA
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lst={}; Do[If[n==Plus@@Divisors[n]-n-12, AppendTo[lst, n]], {n, 10^4}]; Print[lst];
Select[Range[1, 10^4], DivisorSigma[1, #] - 2 # == 12 &] (* Vincenzo Librandi, Sep 14 2016 *)
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PROG
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(MAGMA) [n: n in [1..1400] | (SumOfDivisors(n)-2*n) eq 12]; // Vincenzo Librandi, Sep 14 2016
(PARI) is(n)=sigma(n)==2*n+12 \\ Charles R Greathouse IV, Feb 21 2017
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CROSSREFS
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Cf. A000203, A005101, A141549 (deficiency 12).
Sequence in context: A125639 A076496 A125640 * A106682 A228875 A175258
Adjacent sequences: A141542 A141543 A141544 * A141546 A141547 A141548
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KEYWORD
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nonn
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AUTHOR
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Vladimir Joseph Stephan Orlovsky, Aug 16 2008
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STATUS
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approved
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