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

1, 5, 10, 17, 31, 42, 55, 75, 92, 111, 139, 162, 187, 233, 262, 293, 337, 372, 409, 461, 502, 545, 615, 662, 711, 779, 832, 887, 963, 1022, 1083, 1181, 1246, 1313, 1405, 1476, 1549, 1649, 1726, 1805, 1951, 2034, 2119, 2235, 2324, 2415, 2539, 2634, 2731, 2885

Offset: 1

Author

David Brown, Mar 06 2010

Keywords

• nonn

Crossrefs

Cf. A174063, A174094.

Row sums of triangle A174063. [David Brown, Mar 20 2010]

Programs

Maple

f:= proc(N) local i,j,obj,cons;
obj:= add(i*x[i],i=1..2*N-1);
cons:= {seq(seq(x[i]+x[j]<=1, j=2*i..2*N-1, i),i=1..N),
add(x[i],i=1..2*N-1)=N};
Optimization:-Minimize(obj,cons,assume=binary)[1]
end proc:
map(f, [$1..60]); # Robert Israel, May 06 2019

Mathematica

a[n_] := Module[{obj, cons},
obj = Sum[i*x[i], {i, 1, 2n-1}];
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];
Minimize[{obj, cons}, Array[x, 2n-1], Integers][[1]]];
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 *)

Extensions

Extended by Ray Chandler, Mar 19 2010