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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

%I

%S 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,

%T 14,29,10,31,64,11,68,35,72,37,38,39,80,41,7,43,44,3,23,47,48,49,100,

%U 17,104,53,18,55,28,57,116,59,4,61,31,63,128,65,11,67,136,23,35,71,16,73

%N Numerator of the unitary harmonic mean (i.e., the harmonic mean of the unitary divisors) of the positive integer n.

%C a(A006086(n)) = A006087(n). [_Reinhard Zumkeller_, Mar 17 2012]

%H Reinhard Zumkeller, <a href="/A103339/b103339.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%p 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);

%t 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 *)

%o (Haskell)

%o import Data.Ratio ((%), numerator)

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

%o -- _Reinhard Zumkeller_, Mar 17 2012

%Y Cf. A103340, A099377, A099378.

%Y Cf. A034444, A034448, A077610.

%K frac,nonn

%O 1,2

%A _Emeric Deutsch_, Jan 31 2005

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Last modified March 31 03:48 EDT 2020. Contains 333136 sequences. (Running on oeis4.)