

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
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OFFSET

1,1


COMMENTS

Invented by the HR mathematical theory formation program.


REFERENCES

S. Colton, Unpublished PhD Thesis, University of Edinburgh, 2000


LINKS



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



KEYWORD

easy,nonn


AUTHOR

Simon Colton (simonco(AT)cs.york.ac.uk), Aug 21 2000


EXTENSIONS



STATUS

approved



