

A001600


Harmonic means of divisors of harmonic numbers.
(Formerly M0609 N0220)


9



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
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OFFSET

1,2


COMMENTS

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).


REFERENCES

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).


LINKS

R. J. Mathar, Table of n, a(n) for n = 1..937, extending the former bfile of T. D. Noe.
Marco Abrate, Stefano Barbero, Umberto Cerruti, Nadir Murru, The Biharmonic mean, arXiv:1601.03081 [math.NT], 2016.
G. L. Cohen, Email to N. J. A. Sloane, Apr. 1994
M. Garcia, On numbers with integral harmonic mean, Amer. Math. Monthly 61, (1954). 8996.
Takeshi Goto, All harmonic numbers less than 10^14
Takeshi Goto, Table of a(n) for n=1..937
O. Ore, On the averages of the divisors of a number, Amer. Math. Monthly, 55 (1948), 615619.
O. Ore, On the averages of the divisors of a number (annotated scanned copy)


MATHEMATICA

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]](* JeanFrançois Alcover, May 11 2012 *)


PROG

(Haskell)
a001600 n = a001600_list !! (n1)
a001600_list =
[numerator m  x < [1..], let m = hm x, denominator m == 1] where
hm x = genericLength divs * recip (sum $ map recip divs)
where divs = map fromIntegral $ a027750_row x
 Reinhard Zumkeller, Apr 01 2014
(PARI) lista(nn) = for (n=1, nn, if (denominator(q=n*numdiv(n)/sigma(n)) == 1, print1(q, ", "))); \\ Michel Marcus, Jan 13 2016


CROSSREFS

Cf. A001599, A090240 (sorted values).
Sequence in context: A191665 A254105 A247548 * A175578 A316609 A000036
Adjacent sequences: A001597 A001598 A001599 * A001601 A001602 A001603


KEYWORD

nonn,nice,easy


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from Matthew Conroy, Jan 15 2006


STATUS

approved



