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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323383 Positive integers k such that tau(k) >= k/2. 0
1, 2, 3, 4, 6, 8, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

There are only 7 positive integers which meet this constraint. These happen to be proper divisors of 24. Inductively, there can only be a finite number of integers which meet this constraint. 1 has a perfect tau(k) / k ratio at 1. Every time a j-th power of a prime is multiplied by it, its ratio is multiplied by (j + 1)/p^j. Although 2 also achieves a perfect score, the scores must degrade after 2 because the above ratio is less than 1 otherwise.

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

tau(1) = 1 >= 0.5

tau(2) = 2 >= 1

tau(3) = 2 >= 1.5

tau(4) = 3 >= 2

so 1, 2, 3, 4 are in the sequence.

tau(5) = 2 < 2.5

so 5 is not in the sequence.

MATHEMATICA

Select[Range[10^3], 2 DivisorSigma[0, #] >= # &] (* Michael De Vlieger, Jan 20 2019 *)

PROG

(PARI) for (n = 1, 100, if (sigma(n, 0) >= n / 2, print1(n, ", ")));

CROSSREFS

Cf. A000005.

Cf. A018253 without 24.

Sequence in context: A271487 A211397 A173542 * A085113 A129121 A018556

Adjacent sequences:  A323380 A323381 A323382 * A323384 A323385 A323386

KEYWORD

nonn,full,fini

AUTHOR

Keith J. Bauer, Jan 12 2019

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 December 11 21:21 EST 2019. Contains 329937 sequences. (Running on oeis4.)