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A141545 Numbers n whose abundance is 12: sigma(n) - 2n = 12. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

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

EXAMPLE

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A000203, A005101, A141549 (deficiency 12).

Sequence in context: A125639 A076496 A125640 * A106682 A228875 A175258

Adjacent sequences:  A141542 A141543 A141544 * A141546 A141547 A141548

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Aug 16 2008

STATUS

approved

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Last modified March 30 18:30 EDT 2017. Contains 284302 sequences.