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A064168 Sum of numerator and denominator in n-th harmonic number, 1 + 1/2 + 1/3 +...+ 1/n. 2

%I

%S 2,5,17,37,197,69,503,1041,9649,9901,111431,113741,1506353,1532093,

%T 1556117,3157279,54394463,18358381,352893319,71354639,24031221,

%U 24266365,563299563,1704771547,42976237267,43319457067,392849685203,395718022103,11556136074187

%N Sum of numerator and denominator in n-th harmonic number, 1 + 1/2 + 1/3 +...+ 1/n.

%C Numerator and denominator in definition have no common factors >1.

%H Brian Hayes, <a href="http://bit-player.org/2017/a-tantonalizing-problem">A Tantonalizing Problem</a>

%e The 3rd harmonic number is 11/6. So a(3) = 11 + 6 = 17.

%p h:= n-> numer(sum(1/k,k=1..n))+denom(sum(1/k,k=1..n)): seq(h(n),n=1..30); # _Emeric Deutsch_, Nov 18 2004

%t Table[Numerator[HarmonicNumber[n]] + Denominator[HarmonicNumber[n]], {n, 120}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 06 2011 *)

%t Numerator[#]+Denominator[#]&/@HarmonicNumber[Range[30]] (* _Harvey P. Dale_, Jul 04 2017 *)

%Y Cf. A001008, A002805.

%K nonn,easy

%O 1,1

%A _Leroy Quet_, Sep 19 2001

%E More terms from _Emeric Deutsch_, Nov 18 2004

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Last modified January 22 08:45 EST 2018. Contains 298042 sequences.