A216144 - OEIS

%I #26 Nov 08 2016 16:59:37

%S 2,3,6,15,49,174,715,3115,14937,80435,447840,2724104,17442772,

%T 114379900,784149082,5708691486,43849291331,342473913400,

%U 2803269796342,23620771158595,201815957246322,1793779464521956,16342108667160302,154171144824008980,1518409682511777987

%N Square root of smallest square greater than the product of first n primes.

%C Known values such that a(n)=A145781(n) are a(n)=2,3,6,15 and 715, i.e. for primes p=2,3,5,7 and 17.

%C (The relation a(n)=A145781(n) means that a(n)(a(n)-1) is a primorial number.) - _M. F. Hasler_, Sep 02 2012, - corrected by _Jonathan Sondow_, Sep 02 2012

%H C. Aebi and G. Cairns, <a href="http://www.parabola.unsw.edu.au/vol45_no1/vol45_no1_1.pdf">Partitions of primes</a>, Parabola 45, Issue 1 (2009); see the table on p. 5.

%F a(n)=sqrt(A002110(n) + A145781(n)).

%F a(n)=A060797(n)+1. - _M. F. Hasler_, Sep 02 2012

%e a(2) = sqrt(2*3 + A145781(2))= sqrt(2*3 + 3) = sqrt(9) = 3.

%o (PARI) j=[];for (n=1, 30, p = prod(i=1, n, prime(i)); j=concat(j, floor(sqrt((ceil(sqrt(p))^2))));); j

%o (PARI) A216144(n)=sqrtint(prod(k=1,n,prime(k)))+1 \\ - _M. F. Hasler_, Sep 02 2012

%Y Cf. A002110, A060797, A145781, A215658, A215659.

%K nonn

%O 1,1

%A _Michel Marcus_, Sep 02 2012