

A173490


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


5



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


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. 423426.


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

Cf. A005101, A039725, A005231.
Sequence in context: A177425 A182854 A270660 * A005101 A124626 A231547
Adjacent sequences: A173487 A173488 A173489 * A173491 A173492 A173493


KEYWORD

easy,nonn


AUTHOR

Daniel Forgues, Nov 22 2010


STATUS

approved



