1,2

Square-free kernel of both n! and lcm{1..n}.

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

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

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

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.3, p. 14, "n?".

T. D. Noe, Table of n, a(n) for n=1..400

Eric Weisstein's World of Mathematics, Primorial

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

a := n -> mul(k, k=select(isprime, [$1..n])); [From Peter Luschny (peter(AT)luschny.de), Jun 19 2009]

q#[x_] := Apply[Times, Table[Prime[w], {w, 1, PrimePi[x]}]]; Table[q#[w], {w, 1, 30}

A002110[A000720[n]] = n# = A034386(n)

A007947[ A003418[ n ] ] = A034386[ n ] = A007947[ A000142[ n ] ].

Cf. A002110. Also A007947[ A003418[ n ] ] = A034386[ n ] = A007947[ A000142[ n ] ].

Sequence in context: A147299 A090549 A080326 this_sequence A084343 A083907 A025552

Adjacent sequences: A034383 A034384 A034385 this_sequence A034387 A034388 A034389

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).