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

1,2

Links

Table of n, a(n) for n=1..50.

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 *)

Crossrefs

Cf. A174063, A174094.

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

Sequence in context: A271328 A086653 A215449 * A020642 A067253 A284703

Adjacent sequences: A174059 A174060 A174061 * A174063 A174064 A174065

Keyword

nonn

Author

David Brown, Mar 06 2010

Extensions

Extended by Ray Chandler, Mar 19 2010

Status

approved