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

Author

Irwin Paredes Escobar, Dec 19 2020

Keywords

• nonn
• more

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.

Examples

			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|).