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%I #27 Sep 08 2022 08:45:02
%S 2,8,12,18,24,40,56,60,72,80,84,88,96,104,108,128,132,136,152,156,180,
%T 184,204,228,232,240,248,252,276,288,296,328,344,348,360,372,376,384,
%U 396,424,444,448,450,468,472,480,488,492
%N Even refactorable numbers (i.e., the number of divisors is itself a divisor and it is also even).
%C Invented by the HR mathematical theory formation program.
%D S. Colton, Unpublished PhD Thesis, University of Edinburgh, 2000
%H Amiram Eldar, <a href="/A057265/b057265.txt">Table of n, a(n) for n = 1..10000</a>
%H Simon Colton, <a href="http://www.cs.uwaterloo.ca/journals/JIS/colton/joisol.html">Refactorable Numbers - A Machine Invention</a>, J. Integer Sequences, Vol. 2, 1999, #2.
%H Simon Colton, <a href="http://web.archive.org/web/20070831060523/http://www.dai.ed.ac.uk/homes/simonco/research/hr/">HR - Automatic Theory Formation in Pure Mathematics</a>
%e 18 is refactorable because tau(18) = 6 and 6 divides 18 and 18 is even.
%t rfnQ[n_]:=Module[{ds=DivisorSigma[0,n]},Divisible[n,ds] && EvenQ[ds]];Select[Range[2,500,2],rfnQ] (* _Harvey P. Dale_, Mar 14 2011 *)
%o (Magma) [k:k in [2..500 by 2]| IsIntegral(k/d) and IsEven(d) where d is #Divisors(k)]; // _Marius A. Burtea_, Jan 13 2020
%Y Cf. A033950, A036896.
%K easy,nonn
%O 1,1
%A Simon Colton (simonco(AT)cs.york.ac.uk), Aug 21 2000
%E Corrected (erroneous term 36 removed) by _Harvey P. Dale_, Mar 14 2011
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