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

1,3

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Book Stacking Problem.

Formula

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

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 *)

Prog

(Python)
from sympy import harmonic
def A104174(n): return (lambda x: x.p % x.q)(harmonic(n)) # Chai Wah Wu, Sep 26 2021
(PARI) a(n) = numerator(frac(sum(k=1, n, 1/k))); \\ Michel Marcus, Sep 27 2021

Crossrefs

Cf. A064169, A075135.

Sequence in context: A058352 A376020 A121755 * A050400 A326121 A008971

Adjacent sequences: A104171 A104172 A104173 * A104175 A104176 A104177

Keyword

nonn

Author

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

Status

approved