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Indices of vertex points of the upper convex hull of the squarefree number graph.
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%I #17 Jan 26 2021 11:10:13

%S 1,2,3,7,43,239,1663,9242,47523,351115,2015403,4026914,10143015,

%T 72872619,144151023,413384223

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

%C 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.

%e 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)).

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

%K nonn,more

%O 1,2

%A _Irwin Paredes Escobar_, Dec 19 2020