A338159 - OEIS

%I #29 Dec 23 2020 17:14:12

%S 1,12,60,96,360,576,480,15120,864,2880,3360,6912,25200,7680,20160,

%T 36960,4320,93312,46080,82944,221760,34560,2494800,311040,53760,88200,

%U 15966720,30240,3880800,1995840,43200,322560,388800,345600,970200,241920,414720,5832000,529200,5598720

%N The least number which can be represented as a product of the greatest number of distinct positive integers in exactly n ways.

%C k = p_1^2*p_2*...*p_n obviously has exactly n required representations. Hence a(n) exists for any n.

%C a(n) is the least k such that A338160(k) = n.

%C All terms are in A025487.

%H David A. Corneth, <a href="/A338159/b338159.txt">Table of n, a(n) for n = 1..1283</a> (first 150 terms from Dmitry Khomovsky)

%H David A. Corneth, <a href="/A338159/a338159.gp.txt">More terms</a>

%F a(A338160(n)) = n.

%F A338160(k) <> n for k < a(n).

%e a(60) = 3 because 60 = 2*3*10 = 2*5*6 = 3*4*5 and each number less than 60 does not have exactly 3 such representations (adding the factor 1 to each product doesn't change anything).

%Y Cf. A338160.

%K nonn

%O 1,2

%A _Vladimir Letsko_, Oct 14 2020

%E a(23)-a(40) from _Andrew Howroyd_, Oct 14 2020