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 A090240 Numbers n which occur as the harmonic mean of the divisors of m for some m. 8
 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 19, 21, 24, 25, 26, 27, 29, 31, 35, 37, 39, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 60, 61, 70, 73, 75, 77, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 94, 96, 97, 99, 101, 102, 105, 106, 107, 108, 110, 114, 115 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The equation n = m*tau(m)/sigma(m) has an integer solution m. Here tau(n) (A000005) is the number of divisors of n and sigma(n) is the sum of the divisors of n (A000203). A001600 sorted in order. REFERENCES For further references see A001599. LINKS T. Goto and S. Shibata, All numbers whose positive divisors have integral harmonic mean up to 300, Math. Comput. 73 (2004), 475-491. MATHEMATICA f[n_] := (n*DivisorSigma[0, n]/DivisorSigma[1, n]); a = Table[ 0, {120}]; Do[ b = f[n]; If[ IntegerQ[b] && b < 121 && a[[b]] == 0, a[[b]] = n], {n, 1, 560000000}]; Select[ Range[120], a[[ # ]] > 0 &] (* Robert G. Wilson v, Feb 14 2004 *) CROSSREFS Values of m are in A091911. Cf. A001599, A001600, A090758, A090759, A090760, A090761, A090762. Sequence in context: A119605 A144146 A284763 * A137407 A261406 A264387 Adjacent sequences:  A090237 A090238 A090239 * A090241 A090242 A090243 KEYWORD nonn AUTHOR R. K. Guy, Feb 08 2004 EXTENSIONS More terms from Robert G. Wilson v, Feb 14 2004 STATUS approved

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Last modified May 21 17:51 EDT 2022. Contains 353921 sequences. (Running on oeis4.)