

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.


1



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
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OFFSET

1,1


COMMENTS

Note that s is necessarily a multiple of r.


LINKS



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



KEYWORD

nonn


AUTHOR



STATUS

approved



