OFFSET
1,1
COMMENTS
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.
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
KEYWORD
easy,nonn
AUTHOR
Daniel Forgues, Nov 22 2010
STATUS
approved