%I A034386
%S A034386 1,2,6,6,30,30,210,210,210,210,2310,2310,30030,30030,30030,30030,
%T A034386 510510,510510,9699690,9699690,9699690,9699690,223092870,223092870,
%U A034386 223092870,223092870,223092870,223092870,6469693230,6469693230
%N A034386 Primorial numbers (second definition): n# = product of primes <= n.
%C A034386 Square-free kernel of both n! and lcm{1..n}.
%C A034386 a(n)=lcm{ core(1),core(2),core(3),...,core(n)} where core(x) denotes 
               the square-free part of x, the smallest integer such that xcore(x) 
               is a square. - Benoit Cloitre (benoit7848c(AT)orange.fr), May 31 
               2002
%C A034386 The sequence can also be obtained by taking a(1) = 1 and then multiplying 
               the previous term by n if n is coprime to the previous term a(n-1) 
               and taking a(n) = a(n-1) otherwise. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), 
               Oct 30 2002; corrected by Franklin T. Adams-Watters, Dec 13 2006
%C A034386 If n = a(n-1) + 1, then n is prime. However, this is only satisfied for 
               trivial cases n=2 and n=3. - Matthew Flaschen (matthew.flaschen(AT)gatech.edu), 
               May 24 2008
%D A034386 S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.3, p. 
               14, "n?".
%H A034386 T. D. Noe, <a href="b034386.txt">Table of n, a(n) for n=1..400</a>
%H A034386 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Primorial.html">Primorial</a>
%F A034386 Asymptotic expression for a(n): exp((1 + o(1)) * n) where o(1) is the 
               "little o" notation - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), 
               Apr 08 2001
%p A034386 a := n -> mul(k,k=select(isprime,[$1..n])); [From Peter Luschny (peter(AT)luschny.de), 
               Jun 19 2009]
%t A034386 q#[x_] := Apply[Times, Table[Prime[w], {w, 1, PrimePi[x]}]]; Table[q#[w], 
               {w, 1, 30}
%Y A034386 A002110[A000720[n]] = n# = A034386(n)
%Y A034386 A007947[ A003418[ n ] ] = A034386[ n ] = A007947[ A000142[ n ] ].
%Y A034386 Cf. A002110. Also A007947[ A003418[ n ] ] = A034386[ n ] = A007947[ A000142[ 
               n ] ].
%Y A034386 Sequence in context: A147299 A090549 A080326 this_sequence A084343 A083907 
               A025552
%Y A034386 Adjacent sequences: A034383 A034384 A034385 this_sequence A034387 A034388 
               A034389
%K A034386 nonn,easy,nice
%O A034386 1,2
%A A034386 N. J. A. Sloane (njas(AT)research.att.com).