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%I #26 Mar 11 2024 04:17:31
%S 12,18,20,24,30,36,40,42,48,54,56,60,66,70,72,78,80,84,88,90,96,100,
%T 102,104,108,112,114,120,126,132,138,140,144,150,156,160,162,168,174,
%U 176,180,186,192,196,198,200,204,208,210,216,220,222,224,228,234,240
%N Even abundant numbers (even numbers n whose sum of divisors exceeds 2n).
%C Set difference of abundant numbers A005101 by odd abundant numbers A005231.
%C 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.
%C 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
%C 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
%H T. D. Noe, <a href="/A173490/b173490.txt">Table of n, a(n) for n = 1..10000</a>
%H L. E. Dickson, <a href="http://www.jstor.org/stable/2370406">Even abundant numbers</a>, American Journal of Mathematics 35 (1913), pp. 423-426.
%F a(n) = 2 * A039725(n). - _Amiram Eldar_, Mar 11 2024
%t Select[2*Range[150], DivisorSigma[1, #] > 2 # &] (* _T. D. Noe_, Jun 25 2012 *)
%o (PARI) is(n)=n%2==0 && sigma(n,-1)>2 \\ _Charles R Greathouse IV_, Feb 21 2017
%Y Cf. A005101, A005231, A039725, A302991, A322287.
%K easy,nonn
%O 1,1
%A _Daniel Forgues_, Nov 22 2010
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