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A120358
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Even refactorable numbers k such that the number r of odd divisors and the number s of even divisors are both odd divisors of k and k is the first number for which the triple (r,s,t) occurs, where t is the number of divisors of k.
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2
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2, 18, 72, 450, 1250, 4050, 16200, 52488, 56448, 64800, 71442, 101250, 198450, 235298, 285768, 328050, 405000, 793800, 1036800, 1312200, 1620000, 1786050, 3175200, 4572288, 4961250, 5248800, 7144200, 12700800, 14289858, 15059072, 16074450, 19845000, 24012450, 25920000, 28576800
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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 and t = r+s = 6.
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MATHEMATICA
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seq[kmax_] := Module[{triples = {}, v = {}, r, s, t}, Do[t = DivisorSigma[0, k]; r = t - DivisorSigma[0, k/2]; s = t - r; If[OddQ[r] && OddQ[s] && FreeQ[triples, {r, s, t}] && Divisible[k, t] && Divisible[k, r] && Divisible[k, s], AppendTo[v, k]; AppendTo[triples, {r, s, t}]], {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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