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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

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 | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 23 15:08 EST 2014. Contains 249851 sequences.