A128437 a(n) = floor((numerator of H(n))/n), where H(n) = Sum_{k=1..n} 1/k is the n-th harmonic number.

1, 1, 3, 6, 27, 8, 51, 95, 792, 738, 7610, 7168, 88153, 83695, 79717, 152284, 2478954, 793016, 14489252, 2791756, 898002, 867872, 19318117, 56159289, 1362100898, 1322913164, 11575416740, 11264449603, 318174017634, 310156094338

Offset: 1

Author

Leroy Quet, Mar 03 2007

Keywords

• nonn

Comments

Numerator of H(n) is a(n)*n + A126083(n).

Examples

			a(6) = 8 because H(6) = 49/20 and floor(49/6) = 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2310

Crossrefs

Cf. A128438, A001008, A126083.

Programs

Maple

H:=n->sum(1/k,k=1..n): a:=n->floor(numer(H(n))/n): seq(a(n),n=1..35); # Emeric Deutsch, Mar 22 2007

Mathematica

seq = {}; s = 0; Do[s += 1/n; AppendTo[seq, Floor[Numerator[s]/n]], {n, 1, 30}]; seq (* Amiram Eldar, Dec 01 2020 *)

PARI

a(n) = numerator(sum(k=1, n, 1/k))\n; \\ Michel Marcus, Feb 01 2019

Python

from sympy import harmonic
def A128437(n): return harmonic(n).p//n # Chai Wah Wu, Sep 27 2021

Extensions

More terms from Emeric Deutsch, Mar 22 2007