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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.
3
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
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
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Jan 24 2024
STATUS
approved