A358392 Number of nonempty subsets of {1, 2, ..., n} with GCD equal to 1 and containing the sum of any two elements whenever it is at most n.

1, 1, 2, 3, 7, 9, 19, 27, 46, 63, 113, 148, 253, 345, 539, 734, 1198, 1580, 2540, 3417, 5233, 7095, 11190, 14720, 22988, 31057, 47168, 63331, 98233, 129836, 200689, 269165, 406504, 546700, 838766, 1108583, 1700025, 2281517, 3437422, 4597833, 7023543, 9308824, 14198257, 18982014, 28556962

Offset: 1

Author

Max Alekseyev, Nov 13 2022

Keywords

• nonn

Comments

Also, the number of distinct numerical semigroups that are generated by some subset of {1, 2, ..., n} and have a finite complement in the positive integers.

Links

• Max Alekseyev, Table of n, a(n) for n = 1..100
• Marcel K. Goh et al., Counting numerical semigroups by largest element of minimal generating set, MathOverflow, 2022.

Crossrefs

Inverse Moebius transform of A103580.

Cf. A007865, A050291, A051026, A085489, A139384, A151897, A308546, A326020, A326076, A326080, A326083, A326114.

Formula

a(n) = Sum_{k=1..n} moebius(k) * A103580(floor(n/k)).