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A060797 Integer part of square root of n-th primorial, A002110(n). 9

%I

%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.

%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) has always 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_ *)

%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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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)