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

1,3

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A128438, A001008, A126083.

Sequence in context: A005646 A033194 A304051 * A200654 A208665 A256762

Adjacent sequences: A128434 A128435 A128436 * A128438 A128439 A128440

Keyword

nonn

Author

Leroy Quet, Mar 03 2007

Extensions

More terms from Emeric Deutsch, Mar 22 2007

Status

approved