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A120361
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Even refactorable numbers k such that the number r of odd divisors of k and the number s of even divisors of k are both odd divisors of k.
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4
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2, 18, 72, 450, 882, 1250, 2178, 3042, 4050, 5202, 6498, 9522, 11250, 13122, 15138, 16200, 17298, 24642, 30258, 33282, 39762, 45000, 50562, 52488, 56448, 62658, 64800, 66978, 71442, 80802, 90738, 95922, 101250, 112338, 124002, 142578, 169362, 180000, 183618, 190962, 198450, 206082
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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(2) = 18 since r = 3, s = 3, t = r+s = 6.
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MATHEMATICA
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seq[kmax_] := Module[{v = {}, r, s, t}, Do[t = DivisorSigma[0, k]; r = t - DivisorSigma[0, k/2]; s = t - r; If[OddQ[r] && OddQ[s] && Divisible[k, t] && Divisible[k, r] && Divisible[k, s], AppendTo[v, k]], {k, 2, kmax, 2}]; v]; seq[10^6] (* Amiram Eldar, Aug 01 2024 *)
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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