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 A051014 Nondividing sets on {1,2,...,n}. 3
 1, 2, 3, 5, 7, 11, 14, 21, 27, 38, 52, 73, 90, 123, 159, 211, 263, 344, 413, 535, 658, 832, 1026, 1276, 1499, 1846, 2226, 2708, 3229, 3912, 4592, 5541, 6495, 7795, 9207, 10908, 12547, 14852, 17358, 20493, 23709, 27744, 31921, 37250, 43013, 49936, 57319, 66318 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A set is called nondividing if no element divides the sum of any nonempty subset of the other elements. LINKS Eric Weisstein's World of Mathematics, Nondividing Set EXAMPLE a(5) = 11 because there are 11 nondividing subsets of {1,2,3,4,5}: {}, {1}, {2}, {3}, {4}, {5}, {2,3}, {2,5}, {3,4}, {3,5}, {4,5}. a(7) = 21: {}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {2,3}, {2,5}, {2,7}, {3,4}, {3,5}, {3,7}, {4,5}, {4,6}, {4,7}, {5,6}, {5,7}, {6,7}, {4,6,7}. MAPLE sums:= proc(s) option remember; local i, m;           m:= max(s[]);          `if`(m<1, {}, {m, seq([i, i+m][], i=sums(s minus {m}))})        end: b:= proc(i, s) option remember; local j, ok, t, si;       if i<2 then 1     else si:= s union {i};          ok:= true;          for j in sums(si) while ok do            for t in si while ok do              if irem(j, t)=0 and t<>j then ok:= false fi            od          od;          b(i-1, s) +`if`(ok, b(i-1, si), 0)       fi     end: a:= n-> `if`(n=0, 1, 1+b(n, {})): seq(a(n), n=0..25);  # Alois P. Heinz, Mar 08 2011 MATHEMATICA sums[s_] := sums[s] = Module[{m=Max[s]}, If[m<1, {},   Join[{m},   Sequence@@Table[{i, i+m}, {i, sums[DeleteCases[s, m]]}]]] ]; b[i_, s_] := b[i, s] = Module[{ ok, si, sij, sik}, If[ i<2, 1, si = Union[s, {i}]; ok = True; For[j=1, j <= Length[sums[si]] && ok, j++,   sij = sums[si][[j]];   For[k=1, k <= Length[si] && ok, k++,     If[Divisible[sij, sik=si[[k]]]&&sij!=sik, ok=False]]];     b[i-1, s] + If[ok, b[i-1, si], 0]   ] ]; a[n_] := a[n] = If[n==0, 1, 1+b[n, {}]]; Table[ Print[ a[n] ]; a[n], {n, 0, 47}] (* Jean-François Alcover, Oct 10 2012, after Alois P. Heinz *) CROSSREFS Row sums of A187489.  Cf. A068063. Sequence in context: A051056 A055803 A023027 * A035968 A112581 A288255 Adjacent sequences:  A051011 A051012 A051013 * A051015 A051016 A051017 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from David Wasserman, Feb 15 2002 a(41)-a(47) from Alois P. Heinz, Mar 08 2011 STATUS approved

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Last modified September 20 18:26 EDT 2018. Contains 315240 sequences. (Running on oeis4.)