login
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.
4

%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