A107610 Least number k such that round(k/pi(k)) = n.

2, 16, 56, 190, 556, 1821, 4928, 14136, 39017, 107405, 291330, 791513, 2148323, 5797898, 15726486, 42605113, 115371428, 312629484, 847000031, 2295700537, 6223257066, 16874397811, 45764114391, 124142354193, 336811260666

Offset: 2

Author

Jonathan Vos Post and Robert G. Wilson v, May 17 2005

Keywords

• nonn

Comments

a(n) is the index of the first occurrence of n in A107609.

Lim_{n->infinity} a(n+1)/a(n) ~ e.

Examples

			a(2) = 16 because round(16/pi(16)) = round(16/6) = 3 and for no number less than 16 does the quotient equal 3.
		

Crossrefs

Cf. A000720, A107609, A107614, A272231.

Programs

Mathematica

f[n_] := Round[ n / PrimePi[ n]]; g[2] = 2; g[n_] := g[n] = Block[{k = PrimePi[E g[n - 1]]}, While[ f[k] < n, k++ ]; k]; Do[ Print[ g[ n]], {n, 2, 26}]

Formula

a(n) = min { k >= 2 : round(k/pi(k)) = n }.