|
%I #21 Oct 20 2021 19:26:03
%S 1,4,3,12,5,2,7,32,27,20,11,18,13,7,5,80,17,36,19,20,21,22,23,16,75,
%T 52,27,3,29,10,31,64,11,68,35,324,37,38,39,32,41,7,43,22,45,23,47,120,
%U 49,100,17,156,53,18,55,56,57,116,59,30,61,31,189,448,65,11,67,68,23,35
%N Numerators of the harmonic means of the divisors of the positive integers.
%H Ivan Neretin, <a href="/A099377/b099377.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OresConjecture.html">Ore's Conjecture</a>
%e 1, 4/3, 3/2, 12/7, 5/3, 2, 7/4, 32/15, ...
%t f[n_] := DivisorSigma[0, n]/Plus @@ (1/Divisors@n); Numerator@ Array[f, 70] (* _Robert G. Wilson v_, Aug 04 2010 *)
%t Table[Numerator[DivisorSigma[0, n]/DivisorSigma[-1, n]], {n, 70}] (* _Ivan Neretin_, Nov 13 2016 *)
%o (PARI) a(n) = my(d=divisors(n)); numerator(#d/sum(k=1, #d, 1/d[k])); \\ _Michel Marcus_, Nov 13 2016
%o (Python)
%o from sympy import gcd, divisor_sigma
%o def A099377(n): return (lambda x, y: y*n//gcd(x,y*n))(divisor_sigma(n),divisor_sigma(n,0)) # _Chai Wah Wu_, Oct 20 2021
%Y Cf. A099378.
%K nonn,frac
%O 1,2
%A _Eric W. Weisstein_, Oct 13 2004
%E More terms from _Robert G. Wilson v_, Aug 04 2010
|
