A120356 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.

12, 24, 80, 180, 240, 360, 480, 720, 896, 1344, 1440, 1620, 2688, 3240, 3360, 4032, 5040, 6720, 6912, 8064, 10080, 13440, 20160, 20412, 24300, 25200, 30000, 30240, 34560, 40320, 40824, 48600, 56320, 56700, 60000, 60480, 62208, 67584, 69120

Offset: 1

Author

Walter Kehowski, Jun 25 2006

Keywords

• nonn

Comments

Note that s is necessarily a multiple of r.

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500

Crossrefs

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

Programs

Mathematica

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 *)