login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A335318 Harmonic numbers (A001599) k with a record abundancy index sigma(k)/k. 2
1, 6, 140, 270, 672, 8190, 30240, 332640, 14303520, 17428320, 27027000, 191711520, 2144862720, 3506025600, 5943057120, 14378364000, 45578332800, 288662774400, 505159855200, 2020639420800, 10680522652800, 54557264361600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The corresponding record values are 1, 2, 2.4, 2.666..., 3, 3.2, 4, 4.363..., ...

The terms 1, 6, 672 and 30240 are multiply perfect numbers (A007691) with abundancy indices 1, 2, 3, and 4, respectively. There is no 5-multiperfect number (A046060) in this sequence since A046060(1) = 14182439040 is larger than the harmonic number 5943057120 which is 5-abundant, having an abundancy index 5.067...

LINKS

Table of n, a(n) for n=1..22.

EXAMPLE

The first 7 harmonic numbers are 1, 6, 28, 140, 270, 496 and 672. Their abundancy indices are 1, 2, 2, 2.4, 2.666..., 2 and 3. The record values, 1, 2, 2.4, 2.666... and 3 occur at 1, 6, 140, 270 and 672, the first 5 terms of this sequence.

MATHEMATICA

rm = 0; s = {}; Do[h = DivisorSigma[0, n]/(r = DivisorSigma[1, n]/n); If[IntegerQ[h] && r > rm, rm = r; AppendTo[s, n]], {n, 1, 10^6}]; s

CROSSREFS

Cf. A000203, A001599, A335316, A335317.

Sequence in context: A288565 A090944 A007340 * A342358 A122483 A335369

Adjacent sequences:  A335315 A335316 A335317 * A335319 A335320 A335321

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, May 31 2020

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 16:09 EDT 2021. Contains 345063 sequences. (Running on oeis4.)