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

1,1

Comments

Note that s is necessarily a multiple of r.

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A196812 A163102 A073976 * A120358 A152887 A098817

Adjacent sequences: A120358 A120359 A120360 * A120362 A120363 A120364

Keyword

nonn,changed

Author

Walter Kehowski, Jun 25 2006

Extensions

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

Status

approved