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%I #36 Nov 22 2023 12:31:14
%S 1,1,2,5,14,48,173,714,3114,14936,80434,447839,2724103,17442771,
%T 114379899,784149081,5708691485,43849291330,342473913399,
%U 2803269796341,23620771158594,201815957246321,1793779464521955,16342108667160301,154171144824008979
%N Integer part of square root of n-th primorial, A002110(n).
%C Integer part of square root of product of n first primes.
%H Soumyadeep Dhar, <a href="/A060797/b060797.txt">Table of n, a(n) for n = 0..632</a>
%F a(n) = A000196(A002110(n)) = floor(sqrt(A002110(n))).
%e 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.
%e (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
%t a = {}; Do[b = 1; Do[b = b Prime[x], {x, 1, n}]; AppendTo[a, Floor[b^(1/2)]], {n, 1, 100}]; a (* _Artur Jasinski_ *)
%t Join[{1},Floor[Sqrt[#]]&/@FoldList[Times,Prime[Range[30]]]] (* _Harvey P. Dale_, Nov 22 2023 *)
%o (PARI) A060797(n)=sqrtint(prod(k=1, n, prime(k))) \\ _M. F. Hasler_, Sep 02 2012
%Y Cf. A060755, A000196, A033677.
%Y Cf. A002110, A060797, A127600.
%K nonn
%O 0,3
%A _Labos Elemer_, Apr 27 2001
%E a(23) correction by _Hans Havermann_, Dec 02 2010
%E Extended to a(0)=1=sqrt(A002110(0)) by _M. F. Hasler_, Sep 02 2012
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