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 A173490 Even abundant numbers (even numbers n whose sum of divisors exceeds 2n). 5

%I

%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 232th 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

%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.

%t Select[2*Range[150], DivisorSigma[1, #] > 2 # &] (* _T. D. Noe_, Jun 25 2012 *)

%Y Cf. A005101, A039725, A005231.

%K easy,nonn

%O 1,1

%A _Daniel Forgues_, Nov 22 2010

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