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A103340 Denominator of the unitary harmonic mean (i.e., the harmonic mean of the unitary divisors) of the positive integer n. 3
1, 3, 2, 5, 3, 1, 4, 9, 5, 9, 6, 5, 7, 3, 2, 17, 9, 5, 10, 3, 8, 9, 12, 3, 13, 21, 14, 5, 15, 3, 16, 33, 4, 27, 12, 25, 19, 15, 14, 27, 21, 2, 22, 15, 1, 9, 24, 17, 25, 39, 6, 35, 27, 7, 18, 9, 20, 45, 30, 1, 31, 12, 20, 65, 21, 3, 34, 45, 8, 9, 36, 5, 37, 57, 26, 25, 24, 7, 40, 51, 41, 63 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(A006086(n)) = 1. [Reinhard Zumkeller, Mar 17 2012]

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

1, 4/3, 3/2, 8/5, 5/3, 2;

a(8) = 9 because the unitary divisors of 8 are {1,8} and 2/(1/1 + 1/8) = 16/9.

MAPLE

with(numtheory): udivisors:=proc(n) local A, k: A:={}: for k from 1 to tau(n) do if gcd(divisors(n)[k], n/divisors(n)[k])=1 then A:=A union {divisors(n)[k]} else A:=A fi od end: utau:=n->nops(udivisors(n)): usigma:=n->sum(udivisors(n)[j], j=1..nops(udivisors(n))): uH:=n->n*utau(n)/usigma(n):seq(denom(uH(n)), n=1..90);

MATHEMATICA

ud[n_] := 2^PrimeNu[n]; usigma[n_] := DivisorSum[n, If[GCD[#, n/#] == 1, #, 0]&]; a[1] = 1; a[n_] := Denominator[n*ud[n]/usigma[n]]; Array[a, 100] (* Jean-Fran├žois Alcover, Dec 03 2016 *)

PROG

(Haskell)

import Data.Ratio ((%), denominator)

a103340 = denominator . uhm where uhm n = (n * a034444 n) % (a034448 n)

-- Reinhard Zumkeller, Mar 17 2012

CROSSREFS

Cf. A103339, A099377, A099378.

Cf. A034444, A034448, A077610.

Sequence in context: A324549 A152178 A274164 * A106615 A194736 A130299

Adjacent sequences:  A103337 A103338 A103339 * A103341 A103342 A103343

KEYWORD

frac,nonn

AUTHOR

Emeric Deutsch, Jan 31 2005

STATUS

approved

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Last modified April 10 02:15 EDT 2020. Contains 333392 sequences. (Running on oeis4.)