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
Keywords
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
Programs
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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
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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
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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
Comments