A120358 Even refactorable numbers k such that the number r of odd divisors and the number s of even divisors are both odd divisors of k and k is the first number for which the triple (r,s,t) occurs, where t is the number of divisors of k.

2, 18, 72, 450, 1250, 4050, 16200, 52488, 56448, 64800, 71442, 101250, 198450, 235298, 285768, 328050, 405000, 793800, 1036800, 1312200, 1620000, 1786050, 3175200, 4572288, 4961250, 5248800, 7144200, 12700800, 14289858, 15059072, 16074450, 19845000, 24012450, 25920000, 28576800

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 and t = r+s = 6.
		

Crossrefs

Cf. A000005, A001227, A033950, A049439, A057265, A120359, A120361, A183063.

Programs

Mathematica

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

Extensions

a(27)-a(35) from Amiram Eldar, Aug 01 2024