A072486 a(1) = 1, a(n) = a(n-1) times smallest prime factor of n.

1, 2, 6, 12, 60, 120, 840, 1680, 5040, 10080, 110880, 221760, 2882880, 5765760, 17297280, 34594560, 588107520, 1176215040, 22348085760, 44696171520, 134088514560, 268177029120, 6168071669760, 12336143339520, 61680716697600

Offset: 1

Author

Amarnath Murthy, Jul 13 2002

Keywords

• nonn

Comments

a(n) is the product of the smallest divisors > 1 of all the numbers from 2 to n.

Examples

			a(5) = 60. a(6) = 1*2*3*2*5*2 = 120. Also a(6) = a(5) * 2 = 120.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A020639, A104350.

Programs

Haskell

a072486 n = a072486_list !! (n-1)
a072486_list = scanl1 (*) a020639_list
-- Reinhard Zumkeller, Apr 10 2014

Mathematica

a = {1}; Do[AppendTo[a, a[[n - 1]] FactorInteger[n][[1, 1]]], {n, 2, 25}]; a (* Michael De Vlieger, Aug 25 2015 *)
nxt[{n_,a_}]:={n+1,a*FactorInteger[n+1][[1,1]]}; NestList[nxt,{1,1},30][[All,2]] (* Harvey P. Dale, May 03 2018 *)

PARI

al(n)=local(v=vector(n));v[1]=1;for(k=2,n,v[k]=v[k-1]*factor(k)[1,1]);v  \\ Franklin T. Adams-Watters, Jan 13 2012

PARI

A072486(n)=prod(k=2,n,factor(k)[1,1])  \\ M. F. Hasler, Jan 13 2012

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 25 2003