

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
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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



FORMULA



MATHEMATICA

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


PROG



CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



