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A141545 Numbers k whose abundance is 12: sigma(k) - 2*k = 12. 6
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
From Tomohiro Yamada, Jan 01 2023: (Start)
6p belongs to this sequence if p > 3 is prime since sigma(6p) = 12(p + 1) = 12p + 12. Moreover, 2^m * (2^(m+1) - 13) is also a term of this sequence if 2^(m+1) - 13 is prime (m+1 is a term of A096818) since sigma(2^m * (2^(m+1) - 13)) = (2^(m+1) + 1) * (2^(m+1) - 13) = 2^(m+1) * (2^(m+1) - 13) + 12. So 24, 304, 127744, 33501184, and 8589082624 also belong to this sequence.
Problem: is 54 the only term of this sequence which is of neither type given above? (End)
LINKS
Farideh Firoozbakht and 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).
Cf. A076496 (sigma(k) - a*k = 12).
Sequence in context: A347063 A125639 A125640 * A106682 A334790 A228875
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)