A146323 a(n) = floor(Sum_{i=1..n} (1/phi(i))).

1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9

Offset: 1

Author

Ctibor O. Zizka, Oct 30 2008

Keywords

• nonn

Comments

Looking on the number of 1's, 2's, ..., k's in this sequence we obtain the sequence (1,2,4,5,9,16,25,42,72,...). Limit_{k->oo} (number of (k+1)'s / number of(k's)) = sqrt(e).

The limit above is wrong. The correct limit is exp(zeta(6)/(zeta(2)*zeta(3))) = exp(1/A082695) = 1.672818789624... . - Amiram Eldar, Jul 04 2025

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A028415, A048049, A074467, A082695.

Programs

Mathematica

IntegerPart[Accumulate[1/EulerPhi[Range[110]]]] (* Harvey P. Dale, Dec 19 2015 *)

PARI

list(lim) = {my(s = 0); for(k = 1, lim, s += 1/eulerphi(k); print1(floor(s), ", "));} \\ Amiram Eldar, Jul 04 2025

Formula

a(n) = floor(A028415(n)/A048049(n)). - Amiram Eldar, Jul 04 2025