A107610 -id:A107610 - 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}]

A107614 Consider the least number n such that n divided by pi(n) rounded is greater than any previous n; a(n) is the denominator of n/pi(n).

Original entry on oeis.org

1, 6, 16, 42, 101, 280, 657, 1663, 4107, 10229, 25333, 63321, 159135, 399855, 1014612, 2582128, 6592653, 16898891, 43435899, 111985392, 289453817, 749973236, 1947409123, 5067034865, 13208284732, 34487824962, 90192879037

Offset: 2

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

nonn

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

Cf. A000720, A107609, A107610.

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}]; PrimePi[ g[ # ]] & /@ Range[2, 28]

a(n) = A000720(A107610(n)).

cp's OEIS Frontend

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

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