

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 yx = 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]n12, 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



