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A103339 Numerator of the unitary harmonic mean (i.e., the harmonic mean of the unitary divisors) of the positive integer n. 4
1, 4, 3, 8, 5, 2, 7, 16, 9, 20, 11, 12, 13, 7, 5, 32, 17, 12, 19, 8, 21, 22, 23, 8, 25, 52, 27, 14, 29, 10, 31, 64, 11, 68, 35, 72, 37, 38, 39, 80, 41, 7, 43, 44, 3, 23, 47, 48, 49, 100, 17, 104, 53, 18, 55, 28, 57, 116, 59, 4, 61, 31, 63, 128, 65, 11, 67, 136, 23, 35, 71, 16, 73 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(A006086(n)) = A006087(n). [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) = 16 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(numer(uH(n)), n=1..81);

MATHEMATICA

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

PROG

(Haskell)

import Data.Ratio ((%), numerator)

a103339 = numerator . uhm where uhm n = (n * a034444 n) % (a034448 n)

-- Reinhard Zumkeller, Mar 17 2012

CROSSREFS

Cf. A103340, A099377, A099378.

Cf. A034444, A034448, A077610.

Sequence in context: A200345 A021962 A097672 * A092383 A227242 A156028

Adjacent sequences:  A103336 A103337 A103338 * A103340 A103341 A103342

KEYWORD

frac,nonn

AUTHOR

Emeric Deutsch, Jan 31 2005

STATUS

approved

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Last modified February 21 23:41 EST 2020. Contains 332113 sequences. (Running on oeis4.)