A120360 Even refactorable numbers k such that the number of odd divisors of k and the number of even divisors of k are both even divisors of k.

12, 24, 80, 180, 240, 252, 360, 396, 468, 480, 504, 560, 612, 684, 720, 792, 828, 880, 896, 936, 972, 1040, 1044, 1116, 1200, 1224, 1332, 1344, 1360, 1368, 1440, 1476, 1520, 1548, 1620, 1656, 1692, 1840, 1908, 1944, 2000, 2088, 2124, 2196, 2232, 2320

Offset

1,1

Comments

Note that the number of even divisors s is necessarily a multiple of the number of odd divisors r.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

a(1) = 12 since r = 2, s = 4, t = r + s = 6.

Mathematica

oddtau[n_] := DivisorSigma[0, n/2^IntegerExponent[n, 2]]; seqQ[n_] := Module[{d = DivisorSigma[0, n], o = odd[n]}, EvenQ[d] && EvenQ[o] && Divisible[n, d] && Divisible[n, o] && Divisible[n, d - o]]; Select[Range[2, 2320, 2], seqQ] (* Amiram Eldar, Jan 15 2020 *)

Crossrefs

Cf. A033950, A049439, A057265, A120350.

Sequence in context: A001041 A216425 A081751 * A120356 A109745 A364726

Adjacent sequences: A120357 A120358 A120359 * A120361 A120362 A120363

Keyword

nonn

Author

Walter Kehowski, Jun 25 2006

Status

approved