Probably this is a subsequence of A003418 but I do not have a proof at the moment.
Table of n, a(n) for n=1..4.
a(3) = 420 because 420^(1/3) = 7.4888..., 420 is divisible by all of 1,2,3,4,5,6,7 and it is the largest such number with respect to the exponent 1/3.
Sequence in context: A287679 A051009 A324616 * A072446 A220113 A015181
Adjacent sequences: A060939 A060940 A060941 * A060943 A060944 A060945
Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001