A119411 Product of the first prime(n) primes.

6, 30, 2310, 510510, 200560490130, 304250263527210, 1922760350154212639070, 7858321551080267055879090, 267064515689275851355624017992790, 279734996817854936178276161872067809674997230

Offset: 1

Author

Walter Carlini, Jul 26 2006

Keywords

• easy
• nonn

Examples

			a(1) = p(p(1))# = p(2)# (because p(1) = 2 is the first prime number) = 2* 3 = 6 (by the definition of primorial, see A002110); that is, the product of the first 2 prime numbers.
a(2) = p(p(2))# = p(3)# = 2 * 3 * 5 = 30 = the product of the first 3 primes.
a(3) = 2 * 3 * 5 * 7 * 11 = 2310 = the product of the first 5 primes.
a(4) = 2 * 3 * 5 * 7 * 11 * 13 * 17 = 510510 = product of first 7 primes.
		

References

• A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 50.

Crossrefs

Cf. A002110.

Programs

Mathematica

Array[Times @@ Array[Prime, Prime@# ] &, 10] (* Robert G. Wilson v, Jul 27 2006 *)

Formula

a(n) = p(p[n])#, where p[n] is the n-th prime number and where p(m)# is the m-th primorial number (Cf. A002110).

Extensions

a(10) from Robert G. Wilson v, Jul 27 2006