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

1,1

Comments

Note that s is necessarily a multiple of r.

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A216425 A081751 A120360 * A109745 A364726 A226493

Adjacent sequences: A120353 A120354 A120355 * A120357 A120358 A120359

Keyword

nonn

Author

Walter Kehowski, Jun 25 2006

Status

approved