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

2,1

Comments

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

Links

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

Formula

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

Example

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.

Crossrefs

Cf. A002182, A025487, A354457.

Sequence in context: A188251 A093334 A001816 * A133386 A305624 A056320

Adjacent sequences: A354694 A354695 A354696 * A354698 A354699 A354700

Keyword

nonn,hard

Author

Hugo Pfoertner, Jun 03 2022

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

Status

approved