A104174 Numerator of the fractional part of a harmonic number.

0, 1, 5, 1, 17, 9, 83, 201, 2089, 2341, 551, 2861, 64913, 90653, 114677, 274399, 5385503, 2022061, 42503239, 9276623, 3338549, 3573693, 87368107, 276977179, 7281378067, 7624597867, 71595952403, 74464289303, 2239777822987

Offset: 1

Author

Georg Haass (geha5001(AT)stud.uni-saarland.de), Mar 10 2005

Keywords

• nonn

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Book Stacking Problem.

Crossrefs

Cf. A064169, A075135.

Programs

Mathematica

h[n_] := Sum[1/k, {k, 1, n}]
Table[Numerator[FractionalPart[h[n]]], {n, 1, 30}]
(* Clark Kimberling, Aug 13 2012 *)
FractionalPart[HarmonicNumber[Range[30]]]//Numerator (* Harvey P. Dale, Jul 28 2019 *)

PARI

a(n) = numerator(frac(sum(k=1, n, 1/k))); \\ Michel Marcus, Sep 27 2021

Python

from sympy import harmonic
def A104174(n): return (lambda x: x.p % x.q)(harmonic(n)) # Chai Wah Wu, Sep 26 2021

Formula

a(n) = numerator(frac(Sum_{k=1..n} 1/k)). [edited by Michel Marcus, Sep 27 2021]