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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

LINKS

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

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), Vol 8, No 1 (2016): Serie XII Anno CXXVI.

Hong Liu, Péter Pál Pach, Richárd Palincza, The number of maximum primitive sets of integers, arXiv:1805.06341 [math.CO], 2018.

Sujith Vijay, On large primitive subsets of {1,2,...,2n}, arXiv:1804.01740 [math.CO], 2018.

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

MATHEMATICA

F[S_List, m_] := F[S, m] = Module[{s, S1, S2}, If[Length[S]<m, Return[0]]; If[m == 1, Return[Length[S]]]; s = Min[S]; S1 = S ~Complement~ {s}; S2 = S ~Complement~ Table[j*s, {j, 1, Floor[Max[S]/s]}]; F[S1, m] + F[S2, m - 1]];

a[n_] := F[Range[2n], n];

Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 37}] (* Jean-François Alcover, Jul 10 2018, after Robert Israel *)

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,changed

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

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Last modified July 19 14:33 EDT 2018. Contains 312776 sequences. (Running on oeis4.)