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A354697 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.

%I A354697 #40 May 14 2024 13:40:52
%S A354697 12,120,720,10080,110880,1814400,26611200,518918400,10378368000,
%T A354697 261534873600,5928123801600,168951528345600,4505374089216000,
%U A354697 152056375511040000,4663062182338560000,167870238564188160000,6463004184721244160000,249902828475888107520000,10495918795987300515840000
%N A354697 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 A354697 a(6) <= 110880 = 2*3*6*10*14*22 = 4*5*7*8*9*11.
%H A354697 Zhao Hui Du, <a href="/A354697/b354697.txt">Table of n, a(n) for n = 2..25</a>
%F A354697 A070824(a(n)) >= 2*n.
%e A354697 a(2) = 12 = 2*6 = 3*4,
%e A354697 a(3) = 120 = 2*3*20 = 4*5*6,
%e A354697 a(4) = 720 = 2*4*9*10 = 3*5*6*8,
%e A354697 a(5) = 10080 = 2*3*6*10*28 = 4*5*7*8*9.
%e A354697 a(6) = 110880 = 2*3*6*10*14*22 = 4*5*7*8*9*11.
%e A354697 a(7) = 1814400 = 2*3*4*14*15*18*20 = 5*6*7*8*9*10*12.
%Y A354697 Cf. A002182, A025487, A354457.
%K A354697 nonn,hard
%O A354697 2,1
%A A354697 _Hugo Pfoertner_, Jun 03 2022
%E A354697 a(6) confirmed by and a(7)-a(13) from _David A. Corneth_, Jun 04 2022
%E A354697 a(14) onwards from _Zhao Hui Du_, May 12 2024