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

1,1

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S. Colton, Unpublished PhD Thesis, University of Edinburgh, 2000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