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A102068
a(n) = P(n)!, where P(n) is the largest prime factor of n (with a(1) = 1).
7
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
1,2
COMMENTS
P(n)! is a multiple of n, for almost all n. The exceptions are A057109.
LINKS
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
FORMULA
a(n) = A000142(A006530(n)) = A000040(A061395(n))!.
EXAMPLE
P(12)! = 3! = 6.
MATHEMATICA
Table[FactorInteger[n][[-1, 1]]!, {n, 30}] (* Harvey P. Dale, Jan 29 2014 *)
PROG
(PARI) a(n) = if (n==1, 1, vecmax(factor(n)[, 1])!); \\ Michel Marcus, Sep 24 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Dec 28 2004
STATUS
approved