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The largest highly composite number (A002182) that is prime(n)-smooth.
2

%I #36 Aug 07 2019 08:43:36

%S 1,4,48,720,50400,665280,43243200,2205403200,293318625600,

%T 26985313555200,782574093100800,72779390658374400,8976124847866176000,

%U 368021118762513216000,52222196752400625350400,2454443247362829391468800,1691111397432989450722003200

%N The largest highly composite number (A002182) that is prime(n)-smooth.

%C We assume prime(0) is 1. The set of maximal composite numbers is the "opposite" of the set of (old) prime numbers A008578, with both being indexed by the nonnegative integers A001477.

%H Amiram Eldar, <a href="/A211198/b211198.txt">Table of n, a(n) for n = 0..333</a>

%t (* let t be the sequence of numbers in A002182 *) Join[{1}, Table[Select[t, FactorInteger[#][[-1, 1]] == Prime[n] &][[-1]], {n, 20}]] (* _T. D. Noe_, Feb 09 2013 *)

%Y Cf. A002182.

%K nonn

%O 0,2

%A _Larens Imanyuel_, Feb 03 2013