A121948 Floor of n-th 3-almost prime / n.

8, 6, 6, 5, 5, 4, 4, 5, 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, 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, 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

1,1

Comments

3-almost prime analog of A120927. The division is exact for n = 1, 2, 3, 4. for what n > 9 does a(n) drop below or rise above 4?

The division is exact for n = 1,2,3,4,73,113,163,173,263,499,557; no others up to 10000. First 3 after n=9 is a(109) = floor(435/109). Sequence then mixes 3's and 4's until a(557) = 4. It is then 3 for a long time, although a(812) = floor(3236/812) comes close to 4. Note that lim_{n->infinity} a(n) = infinity, although divergence is very slow. - Franklin T. Adams-Watters, Sep 20 2006

Links

Table of n, a(n) for n=1..105.

Formula

a(n) = floor((n-th 3-almost prime)/n) = floor(A014612(n)/n).

a(n) ~ 2 log n/(log log n)^2. - Charles R Greathouse IV, Feb 05 2017

Example

a(1) = floor(8/1) = floor(8) = 8.
a(2) = floor(12/2) = floor(6) = 6.
a(3) = floor(18/3) = floor(6) = 6.
a(4) = floor(20/4) = floor(5) = 5.
a(5) = floor(27/5) = floor(5.4) = 5.
a(47) = floor(190/47) = floor(4.0425531) = 4.

Crossrefs

Cf. A014612, A120927.

Sequence in context: A067970 A003675 A254290 * A256919 A114141 A089139

Adjacent sequences: A121945 A121946 A121947 * A121949 A121950 A121951

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 04 2006

Extensions

More terms from Franklin T. Adams-Watters, Sep 20 2006

Status

approved