OFFSET
1,3
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
A368372[n_] := Numerator[(n+1)/2 - n/HarmonicNumber[n]];
Array[A368372, 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)).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
(PARI) a368372(n) = numerator((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