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Even refactorable numbers n such that the number r of odd divisors and the number s of even divisors are both even divisors of n and n is the first number for which the triple (r,s,t) occurs, where t is the number of divisors of n.
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%I #8 Jun 13 2020 07:57:31

%S 12,24,80,180,240,360,480,720,896,1344,1440,1620,2688,3240,3360,4032,

%T 5040,6720,6912,8064,10080,13440,20160,20412,24300,25200,30000,30240,

%U 34560,40320,40824,48600,56320,56700,60000,60480,62208,67584,69120

%N Even refactorable numbers n such that the number r of odd divisors and the number s of even divisors are both even divisors of n and n is the first number for which the triple (r,s,t) occurs, where t is the number of divisors of n.

%C Note that s is necessarily a multiple of r.

%H Amiram Eldar, <a href="/A120356/b120356.txt">Table of n, a(n) for n = 1..500</a>

%e a(1)=12 since r=2, s=4 and r+s=6.

%t triples = {}; seq = {}; Do[t = DivisorSigma[0, n]; r = DivisorSigma[0, 2 n] - t; s = t - r; tri = {r, s, t}; If[AllTrue[tri, EvenQ[#] && Divisible[n, #] &] && !MemberQ[triples, tri], AppendTo[seq, n]; AppendTo[triples, tri]], {n, 2, 69120, 2}]; seq (* _Amiram Eldar_, Jun 13 2020 *)

%Y Cf. A001227, A033950, A049439, A057265, A183063.

%K nonn

%O 1,1

%A _Walter Kehowski_, Jun 25 2006