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A173490 Even abundant numbers (even numbers n whose sum of divisors exceeds 2n). 6
12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Set difference of abundant numbers A005101 by odd abundant numbers A005231.
While the first even abundant number is 12 = 2^2*3, the first odd abundant is 945 = 3^3*5*7, the 232nd abundant number! Thus the first 231 terms of this sequence are the same as for sequence A005101 of abundant numbers.
Dickson proves that, for each m and n, there are only a finite number of these numbers having a factor 2^m and n distinct odd prime factors. - T. D. Noe, Mar 31 2011
The asymptotic density of this sequence is in the interval (0.245548, 0.245578) (based on the known bounds on the densities of A005101 and A005231; see A302991 and A322287). - Amiram Eldar, Mar 11 2024
LINKS
L. E. Dickson, Even abundant numbers, American Journal of Mathematics 35 (1913), pp. 423-426.
FORMULA
a(n) = 2 * A039725(n). - Amiram Eldar, Mar 11 2024
MATHEMATICA
Select[2*Range[150], DivisorSigma[1, #] > 2 # &] (* T. D. Noe, Jun 25 2012 *)
PROG
(PARI) is(n)=n%2==0 && sigma(n, -1)>2 \\ Charles R Greathouse IV, Feb 21 2017
CROSSREFS
Sequence in context: A364996 A363082 A270660 * A005101 A124626 A231547
KEYWORD
easy,nonn
AUTHOR
Daniel Forgues, Nov 22 2010
STATUS
approved

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Last modified April 22 21:34 EDT 2024. Contains 371906 sequences. (Running on oeis4.)