cp's OEIS Frontend

A120360 Even refactorable numbers k such that the number of odd divisors of k and the number of even divisors of k are both even divisors of k.

%I A120360 #13 Jan 15 2020 05:50:24
%S A120360 12,24,80,180,240,252,360,396,468,480,504,560,612,684,720,792,828,880,
%T A120360 896,936,972,1040,1044,1116,1200,1224,1332,1344,1360,1368,1440,1476,
%U A120360 1520,1548,1620,1656,1692,1840,1908,1944,2000,2088,2124,2196,2232,2320
%N A120360 Even refactorable numbers k such that the number of odd divisors of k and the number of even divisors of k are both even divisors of k.
%C A120360 Note that the number of even divisors s is necessarily a multiple of the number of odd divisors r.
%H A120360 Amiram Eldar, <a href="/A120360/b120360.txt">Table of n, a(n) for n = 1..10000</a>
%e A120360 a(1) = 12 since r = 2, s = 4, t = r + s = 6.
%t A120360 oddtau[n_] := DivisorSigma[0, n/2^IntegerExponent[n, 2]]; seqQ[n_] := Module[{d = DivisorSigma[0, n], o = odd[n]}, EvenQ[d] && EvenQ[o] && Divisible[n, d] && Divisible[n, o] && Divisible[n, d - o]]; Select[Range[2, 2320, 2], seqQ] (* _Amiram Eldar_, Jan 15 2020 *)
%Y A120360 Cf. A033950, A049439, A057265, A120350.
%K A120360 nonn
%O A120360 1,1
%A A120360 _Walter Kehowski_, Jun 25 2006