login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A179971 Positions of records in the sequence of harmonic means, i.e. in the sequence of rationals A099377(.)/A099378(.). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..53.

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

Cf. A099377, A099378.

Sequence in context: A238616 A093717 A002093 * A067069 A100497 A191283

Adjacent sequences:  A179968 A179969 A179970 * A179972 A179973 A179974

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Aug 04 2010

EXTENSIONS

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 3 18:47 EST 2016. Contains 278745 sequences.