Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Aug 02 2024 01:55:33
%S 2,18,72,450,882,1250,2178,3042,4050,5202,6498,9522,11250,13122,15138,
%T 16200,17298,24642,30258,33282,39762,45000,50562,52488,56448,62658,
%U 64800,66978,71442,80802,90738,95922,101250,112338,124002,142578,169362,180000,183618,190962,198450,206082
%N 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.
%C Note that s is necessarily a multiple of r.
%H Amiram Eldar, <a href="/A120361/b120361.txt">Table of n, a(n) for n = 1..1000</a>
%e a(2) = 18 since r = 3, s = 3, t = r+s = 6.
%t 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 *)
%Y Cf. A000005, A001227, A033950, A049439, A057265, A183063.
%K nonn
%O 1,1
%A _Walter Kehowski_, Jun 25 2006
%E a(36)-a(42) from _Amiram Eldar_, Aug 01 2024