A272231 -id:A272231 - cp's OEIS frontend

A107609 a(n) = round(n / pi(n)) = round(A000027(n) / A000720(n)).

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 2

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

nonn

This sequence grows very slowly. The first n for which a(n) = 5 is 190, then 556 for 6, 1821 for 7, etc. - Alonso del Arte, Feb 27 2012

			a(6) = 2 because pi(6) = 3 and 6/3 = 2.
a(7) = 2 because pi(7) = 4 and 7/4 = 1.75, which rounds up to 2.

Cf. A000720, A107610, A107614, A272231.

Table[ Round[ n / PrimePi[ n]], {n, 2, 106}]

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

Original entry on oeis.org

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

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

nonn

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

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

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

Cf. A000720, A107609, A107614, A272231.

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}]

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

cp's OEIS Frontend

A107609 a(n) = round(n / pi(n)) = round(A000027(n) / A000720(n)).

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