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

2, 5, 17, 37, 197, 69, 503, 1041, 9649, 9901, 111431, 113741, 1506353, 1532093, 1556117, 3157279, 54394463, 18358381, 352893319, 71354639, 24031221, 24266365, 563299563, 1704771547, 42976237267, 43319457067, 392849685203, 395718022103, 11556136074187

Offset

1,1

Comments

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

There is a close relationship between this sequence and the sequence -numerator(H(n-1)*H(n+1)-H(n)^2), where H(n) is the n-th harmonic number. The sequences are an exact match except at indices 1,6,8,21,23,294,300,336,342,847,857,957,967... In these cases, a(n) is an integer multiple of the "determinant" sequence. - Gary Detlefs, Mar 21 2026

Links

Table of n, a(n) for n=1..29.

Brian Hayes, A Tantonalizing Problem

Example

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

Maple

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

Mathematica

Numerator[#]+Denominator[#]&/@HarmonicNumber[Range[30]] (* Harvey P. Dale, Jul 04 2017 *)

Prog

(PARI) a(n) = my(h=sum(k=1, n, 1/k)); numerator(h) + denominator(h); \\ Michel Marcus, Sep 07 2019

Crossrefs

Cf. A001008, A002805, A064167, A064169.

Sequence in context: A276460 A002496 A127436 * A118727 A183906 A042361

Adjacent sequences: A064165 A064166 A064167 * A064169 A064170 A064171

Keyword

nonn,easy

Author

Leroy Quet, Sep 19 2001

Extensions

More terms from Emeric Deutsch, Nov 18 2004

Status

approved