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.

12, 120, 720, 10080, 110880, 1814400, 26611200, 518918400, 10378368000, 261534873600, 5928123801600, 168951528345600, 4505374089216000, 152056375511040000, 4663062182338560000, 167870238564188160000, 6463004184721244160000, 249902828475888107520000, 10495918795987300515840000

Offset: 2

Author

Hugo Pfoertner, Jun 03 2022

Keywords

• nonn
• hard

Comments

a(6) <= 110880 = 2*3*6*10*14*22 = 4*5*7*8*9*11.

Examples

			a(2) = 12 = 2*6 = 3*4,
a(3) = 120 = 2*3*20 = 4*5*6,
a(4) = 720 = 2*4*9*10 = 3*5*6*8,
a(5) = 10080 = 2*3*6*10*28 = 4*5*7*8*9.
a(6) = 110880 = 2*3*6*10*14*22 = 4*5*7*8*9*11.
a(7) = 1814400 = 2*3*4*14*15*18*20 = 5*6*7*8*9*10*12.
		

Links

• Zhao Hui Du, Table of n, a(n) for n = 2..25

Crossrefs

Cf. A002182, A025487, A354457.

Formula

A070824(a(n)) >= 2*n.

Extensions

a(6) confirmed by and a(7)-a(13) from David A. Corneth, Jun 04 2022

a(14) onwards from Zhao Hui Du, May 12 2024