A368373 - OEIS

%I #26 Jan 29 2024 10:38:46

%S 1,6,11,50,137,98,363,1522,7129,14762,83711,172042,1145993,2343466,

%T 1195757,4873118,42142223,28548602,275295799,22334054,18858053,

%U 38186394,444316699,2695645910,34052522467,68791484534,312536252003,630809177806,9227046511387,18609365660294,290774257297357

%N 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.

%H Paolo Xausa, <a href="/A368373/b368373.txt">Table of n, a(n) for n = 1..2000</a>

%e 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, ...

%p AM:=proc(n) local i; (add(i,i=1..n)/n); end;

%p HM:=proc(n) local i; (add(1/i,i=1..n)/n)^(-1); end;

%p s1:=[seq(AM(n)-HM(n),n=1..50)];

%t A368373[n_] := Denominator[(n+1)/2 - n/HarmonicNumber[n]];

%t Array[A368373, 35] (* _Paolo Xausa_, Jan 29 2024 *)

%o (Python)

%o from fractions import Fraction

%o from itertools import count, islice

%o def agen(): # generator of terms

%o     A = H = 0

%o     for n in count(1):

%o         A += n

%o         H += Fraction(1, n)

%o         yield ((A*Fraction(1, n) - n/H)).denominator

%o print(list(islice(agen(), 31))) # _Michael S. Branicky_, Jan 24 2024

%o (Python)

%o from fractions import Fraction

%o from sympy import harmonic

%o def A368373(n): return (Fraction(n+1,2)-Fraction(n,harmonic(n))).denominator # _Chai Wah Wu_, Jan 25 2024

%o (PARI) a368373(n) = denominator((n+1)/2 - n/harmonic(n)) \\ _Hugo Pfoertner_, Jan 25 2024

%Y Cf. A102928/A175441, A368366, A368372.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_, Jan 24 2024