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

Author

Jean-Marc Rebert, Jul 18 2015

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A034386 (primorials), A048764, A249270.

Programs

Mathematica

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

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

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