A260188 Greatest primorial less than or equal to n.

1, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = max_{A034386(i) <= n} A034386(i).

a(n) >> n/log n. - Charles R Greathouse IV, Jul 20 2015

Sum_{n>=1} 1/a(n)^2 = A249270. - Amiram Eldar, Aug 09 2022

Example

a(5) = 2 because 2 is the greatest primorial less than or equal to 5.
a(31) = 30 because 30 is the greatest primorial less than or equal to 31.

Mathematica

Table[k = 0; While[Times @@ Prime@ Range[k + 1] <= n, k++]; Times @@ Prime@ Range@ k, {n, 120}] (* Michael De Vlieger, Aug 30 2016 *)

Prog

(PARI) a(n)=my(t=1, k); forprime(p=2, , k=t*p; if(k>n, return(t), t=k)) \\ Charles R Greathouse IV, Jul 20 2015

Crossrefs

Cf. A034386 (primorials), A048764, A249270.

Sequence in context: A279466 A116863 A136494 * A048764 A327663 A248782

Adjacent sequences: A260185 A260186 A260187 * A260189 A260190 A260191

Keyword

nonn

Author

Jean-Marc Rebert, Jul 18 2015

Status

approved