A120361 Even refactorable numbers k such that the number r of odd divisors of k and the number s of even divisors of k are both odd divisors of k.

2, 18, 72, 450, 882, 1250, 2178, 3042, 4050, 5202, 6498, 9522, 11250, 13122, 15138, 16200, 17298, 24642, 30258, 33282, 39762, 45000, 50562, 52488, 56448, 62658, 64800, 66978, 71442, 80802, 90738, 95922, 101250, 112338, 124002, 142578, 169362, 180000, 183618, 190962, 198450, 206082

Offset: 1

Author

Walter Kehowski, Jun 25 2006

Keywords

• nonn

Comments

Note that s is necessarily a multiple of r.

Examples

			a(2) = 18 since r = 3, s = 3, t = r+s = 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A001227, A033950, A049439, A057265, A183063.

Programs

Mathematica

seq[kmax_] := Module[{v = {}, r, s, t}, Do[t = DivisorSigma[0, k]; r = t - DivisorSigma[0, k/2]; s = t - r; If[OddQ[r] && OddQ[s] && Divisible[k, t] && Divisible[k, r] && Divisible[k, s], AppendTo[v, k]], {k, 2, kmax, 2}]; v]; seq[10^6] (* Amiram Eldar, Aug 01 2024 *)

Extensions

a(36)-a(42) from Amiram Eldar, Aug 01 2024