A270970 Number of subsets of {1,...,n} with sum of elements equal to least common multiple of elements.

1, 2, 4, 5, 6, 8, 9, 11, 14, 16, 17, 21, 22, 24, 28, 31, 32, 37, 38, 53, 56, 57, 58, 71, 72, 73, 77, 85, 86, 131, 132, 138, 141, 142, 143, 163, 164, 165, 167, 289, 290, 310, 311, 316, 403, 404, 405, 454, 455, 458, 460, 463, 464, 478, 479, 557, 559, 560, 561

Offset: 1

Author

Michel Marcus, Mar 27 2016

Keywords

• nonn

Comments

Similar to A270875 but also counts singletons, the trivial solutions.

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A084422, A270875.

Programs

Mathematica

Table[Length@ Select[Rest@ Subsets@ Range@ n, Total@ # == LCM @@ # &], {n, 22}] (* Michael De Vlieger, Mar 27 2016 *)

PARI

a(n) = {nb = 0; S = vector(n, k, k); for (i = 0, 2^n - 1, ss = vecextract(S, i); if (sum(k=1, #ss, ss[k]) == lcm(ss), nb++);); nb;}

Formula

a(n) = A270875(n) + n.

Extensions

a(31)-a(58) from Hiroaki Yamanouchi, Mar 30 2016