A060797 Integer part of square root of n-th primorial, A002110(n).

1, 1, 2, 5, 14, 48, 173, 714, 3114, 14936, 80434, 447839, 2724103, 17442771, 114379899, 784149081, 5708691485, 43849291330, 342473913399, 2803269796341, 23620771158594, 201815957246321, 1793779464521955, 16342108667160301, 154171144824008979

Offset: 0

Author

Labos Elemer, Apr 27 2001

Keywords

• nonn

Comments

Integer part of square root of product of n first primes.

Examples

			n=8, q(8) = 2*3*5*7*11*13*17*19 = 9699690, a(8)=3114. This is between the 128th and 129th divisors of the 8th primorial: 3094 < A000196(9699690)=3114 < 3135.
(In general, x=A002110(n) always has 2^n divisors, and A000196(x) always lies between the k-th and (k+1)-th divisors of x, where k=ceiling(tau(x)/2) and tau(x) is the number of divisors of x.) - _M. F. Hasler_, Sep 02 2012
		

Links

• Soumyadeep Dhar, Table of n, a(n) for n = 0..632

Crossrefs

Cf. A060755, A000196, A033677.

Cf. A002110, A060797, A127600.

Programs

Mathematica

a = {}; Do[b = 1; Do[b = b Prime[x], {x, 1, n}]; AppendTo[a, Floor[b^(1/2)]], {n, 1, 100}]; a (* Artur Jasinski *)
Join[{1},Floor[Sqrt[#]]&/@FoldList[Times,Prime[Range[30]]]] (* Harvey P. Dale, Nov 22 2023 *)

PARI

A060797(n)=sqrtint(prod(k=1, n, prime(k))) \\ M. F. Hasler, Sep 02 2012

Formula

a(n) = A000196(A002110(n)) = floor(sqrt(A002110(n))).

Extensions

a(23) correction by Hans Havermann, Dec 02 2010

Extended to a(0)=1=sqrt(A002110(0)) by M. F. Hasler, Sep 02 2012