A102068 a(n) = P(n)!, where P(n) is the largest prime factor of n (with a(1) = 1).

1, 2, 6, 2, 120, 6, 5040, 2, 6, 120, 39916800, 6, 6227020800, 5040, 120, 2, 355687428096000, 6, 121645100408832000, 120, 5040, 39916800, 25852016738884976640000, 6, 120, 6227020800, 6, 5040, 8841761993739701954543616000000, 120

Offset: 1

Author

Jonathan Sondow, Dec 28 2004

Keywords

• nonn

Comments

P(n)! is a multiple of n, for almost all n. The exceptions are A057109.

Examples

			P(12)! = 3! = 6.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..456
• Paul Erdős and Ilias Kastanas, Solution 6674: The smallest factorial that is a multiple of n, Amer. Math. Monthly 101 (1994) 179.
• A. Ivic, On a problem of Erdos involving the largest prime factor of n, arXiv:math/0311056 [math.NT], 2003-2004.
• Eric Weisstein's World of Mathematics, Greatest Prime Factor
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A000040, A000142, A006530, A057109, A061395, A102067.

Programs

Mathematica

Table[FactorInteger[n][[-1,1]]!,{n,30}] (* Harvey P. Dale, Jan 29 2014 *)

PARI

a(n) = if (n==1, 1, vecmax(factor(n)[,1])!); \\ Michel Marcus, Sep 24 2022

Formula

a(n) = A000142(A006530(n)) = A000040(A061395(n))!.