login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A179971
Positions of records in the sequence of harmonic means, i.e., in the sequence of rationals A099377(.)/A099378(.).
5
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
1,2
LINKS
Eric Weisstein's World of Mathematics, Ore's Conjecture
EXAMPLE
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.
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
CROSSREFS
Sequence in context: A316886 A309943 A002093 * A067069 A100497 A191283
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Aug 04 2010
EXTENSIONS
Definition rephrased by R. J. Mathar, Aug 06 2010
STATUS
approved