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%I #40 May 14 2024 13:40:52
%S 12,120,720,10080,110880,1814400,26611200,518918400,10378368000,
%T 261534873600,5928123801600,168951528345600,4505374089216000,
%U 152056375511040000,4663062182338560000,167870238564188160000,6463004184721244160000,249902828475888107520000,10495918795987300515840000
%N a(n) is the least integer that can be written in two or more ways as the product of the integers in two subsets of its A070824(a(n)) nontrivial divisors, each of size n and with empty intersection.
%C a(6) <= 110880 = 2*3*6*10*14*22 = 4*5*7*8*9*11.
%H Zhao Hui Du, <a href="/A354697/b354697.txt">Table of n, a(n) for n = 2..25</a>
%F A070824(a(n)) >= 2*n.
%e a(2) = 12 = 2*6 = 3*4,
%e a(3) = 120 = 2*3*20 = 4*5*6,
%e a(4) = 720 = 2*4*9*10 = 3*5*6*8,
%e a(5) = 10080 = 2*3*6*10*28 = 4*5*7*8*9.
%e a(6) = 110880 = 2*3*6*10*14*22 = 4*5*7*8*9*11.
%e a(7) = 1814400 = 2*3*4*14*15*18*20 = 5*6*7*8*9*10*12.
%Y Cf. A002182, A025487, A354457.
%K nonn,hard
%O 2,1
%A _Hugo Pfoertner_, Jun 03 2022
%E a(6) confirmed by and a(7)-a(13) from _David A. Corneth_, Jun 04 2022
%E a(14) onwards from _Zhao Hui Du_, May 12 2024
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