A216144 Square root of smallest square greater than the product of first n primes.

2, 3, 6, 15, 49, 174, 715, 3115, 14937, 80435, 447840, 2724104, 17442772, 114379900, 784149082, 5708691486, 43849291331, 342473913400, 2803269796342, 23620771158595, 201815957246322, 1793779464521956, 16342108667160302, 154171144824008980, 1518409682511777987

Offset: 1

Author

Michel Marcus, Sep 02 2012

Keywords

• nonn

Comments

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.

(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

Examples

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

Links

• C. Aebi and G. Cairns, Partitions of primes, Parabola 45, Issue 1 (2009); see the table on p. 5.

Crossrefs

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

Programs

PARI

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

PARI

A216144(n)=sqrtint(prod(k=1,n,prime(k)))+1 \\ - M. F. Hasler, Sep 02 2012

Formula

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

a(n)=A060797(n)+1. - M. F. Hasler, Sep 02 2012