A368373 a(n) = denominator of AM(n)-HM(n), where AM(n) and HM(n) are the arithmetic and harmonic means of the first n positive integers.

1, 6, 11, 50, 137, 98, 363, 1522, 7129, 14762, 83711, 172042, 1145993, 2343466, 1195757, 4873118, 42142223, 28548602, 275295799, 22334054, 18858053, 38186394, 444316699, 2695645910, 34052522467, 68791484534, 312536252003, 630809177806, 9227046511387, 18609365660294, 290774257297357

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..2000

Example

0, 1/6, 4/11, 29/50, 111/137, 103/98, 472/363, 2369/1522, 12965/7129, 30791/14762, 197346/83711, 452993/172042, 3337271/1145993, 7485915/2343466, 4160656/1195757, 18358463/4873118, ...

Maple

AM:=proc(n) local i; (add(i, i=1..n)/n); end;
HM:=proc(n) local i; (add(1/i, i=1..n)/n)^(-1); end;
s1:=[seq(AM(n)-HM(n), n=1..50)];

Mathematica

A368373[n_] := Denominator[(n+1)/2 - n/HarmonicNumber[n]];
Array[A368373, 35] (* Paolo Xausa, Jan 29 2024 *)

Prog

(Python)
from fractions import Fraction
from itertools import count, islice
def agen(): # generator of terms
    A = H = 0
    for n in count(1):
        A += n
        H += Fraction(1, n)
        yield ((A*Fraction(1, n) - n/H)).denominator
print(list(islice(agen(), 31))) # Michael S. Branicky, Jan 24 2024
(Python)
from fractions import Fraction
from sympy import harmonic
def A368373(n): return (Fraction(n+1, 2)-Fraction(n, harmonic(n))).denominator # Chai Wah Wu, Jan 25 2024
(PARI) a368373(n) = denominator((n+1)/2 - n/harmonic(n)) \\ Hugo Pfoertner, Jan 25 2024

Crossrefs

Cf. A102928/A175441, A368366, A368372.

Sequence in context: A269878 A292120 A099437 * A271093 A271291 A271085

Adjacent sequences: A368370 A368371 A368372 * A368374 A368375 A368376

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 24 2024

Status

approved