A173490 Even abundant numbers (even numbers n whose sum of divisors exceeds 2n).

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

Offset: 1

Author

Daniel Forgues, Nov 22 2010

Keywords

• easy
• nonn

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

• T. D. Noe, Table of n, a(n) for n = 1..10000
• L. E. Dickson, Even abundant numbers, American Journal of Mathematics 35 (1913), pp. 423-426.

Crossrefs

Cf. A005101, A005231, A039725, A302991, A322287.

Programs

Mathematica

Select[2*Range[150], DivisorSigma[1, #] > 2 # &] (* T. D. Noe, Jun 25 2012 *)

PARI

is(n)=n%2==0 && sigma(n,-1)>2 \\ Charles R Greathouse IV, Feb 21 2017

Formula

a(n) = 2 * A039725(n). - Amiram Eldar, Mar 11 2024