A120359 Even refactorable numbers k such that the number r of odd divisors is odd, the number s of even divisors is even, both r and s are 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.

36, 3600, 8100, 10000, 26244, 32400, 142884, 202500, 396900, 518400, 656100, 810000, 1587600, 1679616, 2286144, 2624400, 3572100, 6350400, 9144576, 9922500, 12960000, 14288400, 20575296, 25401600, 28579716, 32148900, 39690000, 41990400, 48024900, 57153600, 89302500

Offset: 1

Author

Walter Kehowski, Jun 25 2006

Keywords

• nonn

Comments

Note that s is necessarily a multiple of r.

Examples

			a(1) = 36 since r = 3, s = 6 and t = r+s = 9.
		

Crossrefs

Cf. A000005, A001227, A033950, A049439, A057265, A120358, 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] && EvenQ[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(21)-a(22) inserted and a(24)-a(31) added by Amiram Eldar, Aug 01 2024