A339806 Indices of vertex points of the upper convex hull of the squarefree number graph.

1, 2, 3, 7, 43, 239, 1663, 9242, 47523, 351115, 2015403, 4026914, 10143015, 72872619, 144151023, 413384223

Offset

1,2

Comments

Denoting the number of squarefrees up to n by Q(n), we say (n, Q(n)) is on the upper convex hull of the squarefree number graph if for all integers m_1 < n and all integers m_2 > n, (n, Q(n)) is above the secant line from (m_1, Q(m_1)) to (m_2, Q(m_2)). To determine whether n is the index of a vertex in the upper convex hull, it suffices to only check the record maximum points of Q(m)-6*m/Pi^2.

Links

Table of n, a(n) for n=1..16.

Example

3 is on the upper convex hull because Q(3) = 3 and the secant line from (1,1) or (2,2) to (n,Q(n)) for any n>3 passes below the point (3,Q(3)).

Crossrefs

Cf. A275390 (record values of |Q(m)-6*m/Pi^2|).

Sequence in context: A000946 A367020 A091771 * A072714 A051786 A133400

Adjacent sequences: A339803 A339804 A339805 * A339807 A339808 A339809

Keyword

nonn,more

Author

Irwin Paredes Escobar, Dec 19 2020

Status

approved