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A001600
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Harmonic means of divisors of harmonic numbers.
(Formerly M0609 N0220)
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9
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1, 2, 3, 5, 6, 5, 8, 9, 11, 10, 7, 15, 15, 14, 17, 24, 24, 21, 13, 19, 27, 25, 29, 26, 44, 44, 29, 46, 39, 46, 27, 42, 47, 47, 54, 35, 41, 60, 51, 37, 48, 45, 49, 50, 49, 53, 77, 86, 86, 51, 96, 75, 70, 80, 99, 110, 81, 84, 13, 102, 82, 96, 114, 53, 108, 115, 105, 116, 91, 85, 105
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Values of n*tau(n)/sigma(n) corresponding to terms of A001599, where tau(n) (A000005) is the number of divisors of n and sigma(n) is the sum of the divisors of n (A000203).
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REFERENCES
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Garcia, Mariano; On numbers with integral harmonic mean. Amer. Math. Monthly 61, (1954). 89-96.
O. Ore, On the averages of the divisors of a number, Amer. Math. Monthly, 55 (1948), 615-619.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..115
Matthew M. Conroy, Home page (listed instead of email address)
Takeshi Goto, All harmonic numbers less than 10^14
Takeshi Goto, Table of a(n) for n=1..937
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MATHEMATICA
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A001600 = Reap[Do[tau = DivisorSigma[0, n]; sigma = DivisorSigma[1, n]; h = n*tau/sigma; If[IntegerQ[h], Print[h]; Sow[h]], {n, 1, 90000000}]][[2, 1]](* From Jean-François Alcover, May 11 2012 *)
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CROSSREFS
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Cf. A001599, A090240 (sorted values).
Sequence in context: A072636 A191741 A191665 * A175578 A000036 A165081
Adjacent sequences: A001597 A001598 A001599 * A001601 A001602 A001603
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Matthew Conroy, Jan 15 2006
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STATUS
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approved
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