A368372 a(n) = numerator of AM(n)-HM(n), where AM(n) and HM(n) are the arithmetic and harmonic means of the first n positive integers.

0, 1, 4, 29, 111, 103, 472, 2369, 12965, 30791, 197346, 452993, 3337271, 7485915, 4160656, 18358463, 170991927, 124184839, 1278605110, 110351535, 98802055, 211524139, 2595194516, 16562041459, 219589922071, 464651871609, 2207044831642, 4649180818987, 70862100349605, 148699793966557

Offset: 1

Author

N. J. A. Sloane, Jan 24 2024

Keywords

• nonn
• frac

Examples

			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, ...
		

Links

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

Crossrefs

Cf. A102928/A175441, A368366, A368373.

Programs

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

A368372[n_] := Numerator[(n+1)/2 - n/HarmonicNumber[n]];
Array[A368372, 35] (* Paolo Xausa, Jan 29 2024 *)

PARI

a368372(n) = numerator((n+1)/2 - n/harmonic(n)) \\ Hugo Pfoertner, Jan 25 2024

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)).numerator
print(list(islice(agen(), 30))) # Michael S. Branicky, Jan 24 2024

Python

from fractions import Fraction
from sympy import harmonic
def A368372(n): return (Fraction(n+1,2)-Fraction(n,harmonic(n))).numerator # Chai Wah Wu, Jan 25 2024