A057265 Even refactorable numbers (i.e., the number of divisors is itself a divisor and it is also even).

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

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

Invented by the HR mathematical theory formation program.

Examples

			18 is refactorable because tau(18) = 6 and 6 divides 18 and 18 is even.
		

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• S. Colton, Unpublished PhD Thesis, University of Edinburgh, 2000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

Crossrefs

Cf. A033950, A036896.

Programs

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

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 *)

Extensions

Corrected (erroneous term 36 removed) by Harvey P. Dale, Mar 14 2011