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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

Table of n, a(n) for n=1..69.

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 March 20 19:23 EDT 2019. Contains 321349 sequences. (Running on oeis4.)