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 A057265 Even refactorable numbers (i.e., the number of divisors is itself a divisor and it is also even). 12
 2, 8, 12, 18, 24, 40, 56, 60, 72, 80, 84, 88, 96, 104, 108, 128, 132, 136, 152, 156, 180, 184, 204, 228, 232, 240, 248, 252, 276, 288, 296, 328, 344, 348, 360, 372, 376, 384, 396, 424, 444, 448, 450, 468, 472, 480, 488, 492 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Invented by the HR mathematical theory formation program. REFERENCES S. Colton, Unpublished PhD Thesis, University of Edinburgh, 2000 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Simon Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2. Simon Colton, HR - Automatic Theory Formation in Pure Mathematics EXAMPLE 18 is refactorable because tau(18) = 6 and 6 divides 18 and 18 is even. MATHEMATICA rfnQ[n_]:=Module[{ds=DivisorSigma[0, n]}, Divisible[n, ds] && EvenQ[ds]]; Select[Range[2, 500, 2], rfnQ] (* Harvey P. Dale, Mar 14 2011 *) PROG (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 CROSSREFS Cf. A033950, A036896. Sequence in context: A090772 A046525 A235353 * A099418 A108987 A035405 Adjacent sequences: A057262 A057263 A057264 * A057266 A057267 A057268 KEYWORD easy,nonn AUTHOR Simon Colton (simonco(AT)cs.york.ac.uk), Aug 21 2000 EXTENSIONS Corrected (erroneous term 36 removed) by Harvey P. Dale, Mar 14 2011 STATUS approved

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Last modified September 26 13:48 EDT 2023. Contains 365660 sequences. (Running on oeis4.)