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A120356
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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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1
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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
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1,1
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COMMENTS
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Note that s is necessarily a multiple of r.
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LINKS
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EXAMPLE
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a(1)=12 since r=2, s=4 and r+s=6.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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