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%I #18 Sep 24 2022 05:49:09
%S 1,2,6,2,120,6,5040,2,6,120,39916800,6,6227020800,5040,120,2,
%T 355687428096000,6,121645100408832000,120,5040,39916800,
%U 25852016738884976640000,6,120,6227020800,6,5040,8841761993739701954543616000000,120
%N a(n) = P(n)!, where P(n) is the largest prime factor of n (with a(1) = 1).
%C P(n)! is a multiple of n, for almost all n. The exceptions are A057109.
%H Alois P. Heinz, <a href="/A102068/b102068.txt">Table of n, a(n) for n = 1..456</a>
%H Paul Erdős and Ilias Kastanas, <a href="https://www.jstor.org/stable/2324376">Solution 6674: The smallest factorial that is a multiple of n</a>, Amer. Math. Monthly 101 (1994) 179.
%H A. Ivic, <a href="https://arxiv.org/abs/math/0311056">On a problem of Erdos involving the largest prime factor of n</a>, arXiv:math/0311056 [math.NT], 2003-2004.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GreatestPrimeFactor.html">Greatest Prime Factor</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers.</a>
%F a(n) = A000142(A006530(n)) = A000040(A061395(n))!.
%e P(12)! = 3! = 6.
%t Table[FactorInteger[n][[-1,1]]!,{n,30}] (* _Harvey P. Dale_, Jan 29 2014 *)
%o (PARI) a(n) = if (n==1, 1, vecmax(factor(n)[,1])!); \\ _Michel Marcus_, Sep 24 2022
%Y Cf. A000040, A000142, A006530, A057109, A061395, A102067.
%K nonn
%O 1,2
%A _Jonathan Sondow_, Dec 28 2004
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