A179971 Positions of records in the sequence of harmonic means, i.e., in the sequence of rationals A099377(.)/A099378(.).

1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 48, 60, 72, 84, 90, 108, 120, 144, 168, 180, 240, 336, 360, 420, 480, 504, 630, 720, 840, 1008, 1080, 1260, 1440, 1680, 2160, 2520, 3360, 3780, 3960, 4200, 4320, 4620, 5040, 7560, 9240, 10080, 12600, 13860, 15120

Offset: 1

Author

Robert G. Wilson v, Aug 04 2010

Keywords

• nonn

Examples

			The sequence of harmonic means starts 1 < 4/3 < 3/2 < 12/7, increasing from the first to the fourth, which adds 1 to 4 to the sequence.
The fifth harmonic mean is 5/3, smaller than 12/7 and not a record, so 5 is not in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Ore's Conjecture

Crossrefs

Cf. A099377, A099378.

Programs

Maple

hm := proc(n) option remember; n* numtheory[tau](n)/numtheory[sigma](n) ; end proc:
A179971 := proc(n) option remember; if n = 1 then 1; else for k from procname(n-1)+1 do if hm(k) > hm(procname(n-1)) then return k; end if; end do; end if; end proc:
seq(A179971(n),n=1..40) ; # R. J. Mathar, Aug 06 2010

Mathematica

f[n_] := f[n] = DivisorSigma[0, n]/Plus @@ (1/Divisors@n); k = 1; mx = 0; lst = {}; While[k < 18480, a = f@k; If[a > mx, mx = a; AppendTo[lst, k]]; k++ ]; lst

Extensions

Definition rephrased by R. J. Mathar, Aug 06 2010