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A174062 Least possible sum of exactly n positive integers less than 2n such that none of the n integers divides another.

%I A174062 #12 May 17 2023 14:17:58
%S A174062 1,5,10,17,31,42,55,75,92,111,139,162,187,233,262,293,337,372,409,461,
%T A174062 502,545,615,662,711,779,832,887,963,1022,1083,1181,1246,1313,1405,
%U A174062 1476,1549,1649,1726,1805,1951,2034,2119,2235,2324,2415,2539,2634,2731,2885
%N A174062 Least possible sum of exactly n positive integers less than 2n such that none of the n integers divides another.
%p A174062 f:= proc(N) local i,j,obj,cons;
%p A174062 obj:= add(i*x[i],i=1..2*N-1);
%p A174062 cons:= {seq(seq(x[i]+x[j]<=1, j=2*i..2*N-1, i),i=1..N),
%p A174062 add(x[i],i=1..2*N-1)=N};
%p A174062 Optimization:-Minimize(obj,cons,assume=binary)[1]
%p A174062 end proc:
%p A174062 map(f, [$1..60]); # _Robert Israel_, May 06 2019
%t A174062 a[n_] := Module[{obj, cons},
%t A174062 obj = Sum[i*x[i], {i, 1, 2n-1}];
%t A174062 cons = Append[Flatten[Table[Table[x[i]+x[j] <= 1, {j, 2i, 2n-1, i}], {i, 1, n}], 1], AllTrue[Array[x, 2n-1], 0 <= # <= 1&] && Sum[x[i], {i, 1, 2n-1}] == n];
%t A174062 Minimize[{obj, cons}, Array[x, 2n-1], Integers][[1]]];
%t A174062 Reap[For[n = 1, n <= 50, n++, Print[n, " ", a[n]]; Sow[a[n]]]][[2, 1]]; (* _Jean-François Alcover_, May 17 2023, after _Robert Israel_ *)
%Y A174062 Cf. A174063, A174094.
%Y A174062 Row sums of triangle A174063. [_David Brown_, Mar 20 2010]
%K A174062 nonn
%O A174062 1,2
%A A174062 _David Brown_, Mar 06 2010
%E A174062 Extended by _Ray Chandler_, Mar 19 2010