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!)
A196149 Numbers whose divisors increase by a factor of 3 or less. 4
1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 54, 56, 60, 63, 64, 66, 70, 72, 75, 78, 80, 81, 84, 88, 90, 96, 99, 100, 102, 104, 105, 108, 110, 112, 117, 120, 126, 128, 130, 132, 135, 136, 140, 144, 147, 150 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The polymath8 project led by Terry Tao refers to these numbers as "3-densely divisible". In general they say that n is y-densely divisible if its divisors increase by a factor of y or less, or equivalently, if for every R with 1 <= R <= n, there is a divisor in the interval [R/y,R]. They use this as a weakening of the condition that n be y-smooth. - David S. Metzler, Jul 02 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

T. Tao, A Truncated Elementary Selberg Sieve of Pintz (blog entry defining y-densely divisible)

T. Tao et al.,Polymath8 home page

FORMULA

a(n) = A052287(n) / 3.

EXAMPLE

14 is not a term because its divisors are 1,2,7,14, and the gap from 2 to 7 is more than a factor of 3. - N. J. A. Sloane, Aug 03 2015

MATHEMATICA

dif3[n_]:=Max[#[[2]]/#[[1]]&/@Partition[Divisors[n], 2, 1]]<=3; Select[ Range[ 200], dif3] (* Harvey P. Dale, Jun 08 2015 *)

PROG

(Haskell)

a196149 n = a196149_list !! (n-1)

a196149_list = filter f [1..] where

   f n = all (<= 0) $ zipWith (-) (tail divs) (map (* 3) divs)

                      where divs = a027750_row' n

-- Reinhard Zumkeller, Jun 25 2015, Sep 28 2011

(PARI) is(n)=my(d=divisors(n)); for(i=2, #d, if(d[i]>3*d[i-1], return(0))); 1 \\ Charles R Greathouse IV, Jul 06 2013

CROSSREFS

A174973 is a subsequence.

Cf. A027750.

Sequence in context: A240911 A064150 A259227 * A240163 A269045 A067023

Adjacent sequences:  A196146 A196147 A196148 * A196150 A196151 A196152

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Sep 28 2011

EXTENSIONS

Alternate nomenclature and links added by David S. Metzler, Jul 02 2013

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 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)