OFFSET
0,3
COMMENTS
Integer part of square root of product of n first primes.
LINKS
Soumyadeep Dhar, Table of n, a(n) for n = 0..632
EXAMPLE
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
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 *)
PROG
(PARI) A060797(n)=sqrtint(prod(k=1, n, prime(k))) \\ M. F. Hasler, Sep 02 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 27 2001
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
STATUS
approved