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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A174094 Number of ways to choose n positive integers less than or equal to 2n such that none of the n integers divides another. 4
2, 2, 3, 5, 4, 6, 12, 10, 14, 26, 26, 34, 68, 48, 72, 120, 120, 168, 336, 264, 396, 792, 624, 816, 1632, 1632, 2208, 3616, 3616, 5056, 10112, 6592, 9888, 19776, 19776, 24384, 48768, 48768, 73152, 112320, 76032, 114048, 228096, 190080, 264960, 529920 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) >= 2^(1+floor((n-1)/3)). - Robert Israel, Aug 25 2015

REFERENCES

C. Bindi, L. Bussoli, M. Grazzini, M. Pellegrini, G. Pirillo, M.A. Pirillo, A. Troise, Su un risultato di uno studente di Erdös, Periodico di matematiche 1 (2016), accepted.

LINKS

Marco Pellegrini, Table of n, a(n) for n = 1..100

EXAMPLE

a(1) = 2 because we can choose {1}, {2}.

a(2) = 2 because we can choose {2, 3}, {3, 4}.

a(3) = 3 because we can choose {2, 3, 5}, {3, 4, 5}, {4, 5, 6}.

MAPLE

F:= proc(S, m)

  option remember;

  local s, S1, S2;

  if nops(S) < m then return 0 fi;

  if m = 1 then return nops(S) fi;

  s:= min(S);

  S1:= S minus {s};

  S2:= S minus {seq(j*s, j=1..floor(max(S)/s))};

  F(S1, m) + F(S2, m-1);

end proc;

seq(F({$1..2*n}, n), n=1..37); # Robert Israel, Aug 25 2015

CROSSREFS

The smallest n integers possible is A174063.

Sequence in context: A026399 A117267 A086363 * A284114 A139171 A279724

Adjacent sequences:  A174091 A174092 A174093 * A174095 A174096 A174097

KEYWORD

nonn

AUTHOR

David Brown, Mar 07 2010

EXTENSIONS

More terms from David Brown, Mar 14 2010

a(30)-a(46) from Ray Chandler, Mar 19 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 January 22 22:30 EST 2018. Contains 298093 sequences.