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

1,1

Comments

Note that s is necessarily a multiple of r.

Links

Table of n, a(n) for n=1..35.

Example

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

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 *)

Crossrefs

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

Sequence in context: A163102 A073976 A120361 * A152887 A098817 A197093

Adjacent sequences: A120355 A120356 A120357 * A120359 A120360 A120361

Keyword

nonn,changed

Author

Walter Kehowski, Jun 25 2006

Extensions

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

Status

approved