A339469 a(n) is the smallest k such that k = x_11 * x_12 * x_13 = x_21 * x_22 * x_23 = ... = x_n1 *x_n2 * x_n3 and x_11 + x_12 + x_13 = x_21 + x_22 + x_23 = ... = x_n1 + x_n2 + x_n3; x_ij >= 2.

8, 72, 1200, 37800, 83160, 846720, 1965600, 15724800, 34927200, 279417600, 1437836400, 11502691200, 5751345600, 160626866400, 46010764800, 1927522396800, 8561475468000, 80173757664000

Offset: 1

Author

Ctibor O. Zizka, Dec 06 2020

Keywords

• nonn
• more

Comments

This sequence is defined for n 3-tuples. I have no result for n s-tuples, s >= 4.

Another generalization: For n >= 3, a(n) is the smallest composite k such that k = x_11 * ... * x_1n = x_21 * x_22 * x_2n and x_11 + ... + x_1n = x_21 + x_22 + x_2n; x_ij >= 2.

See A103278 if the requirement of parts >= 2 is dropped. - R. J. Mathar, Dec 11 2020

Examples

			n = 1, k = 8, 8 = 2*2*2 and 2+2+2=6;
n = 2, k = 72, 72 = 6*6*2=8*3*3 and 6+6+2=8+3+3;
n = 3, k = 1200, 1200 = 20*15*4 = 24*10*5 = 25*8*6 and 20+15+4 = 24+10+5 = 25+8+6;
n = 4, k = 37800, 37800 = 54*50*14=63*40*15 = 70*30*18 = 72*25*21 and 54+50+14 = 63+40+15 = 70+30+18 = 72+25+21.
		

Crossrefs

Cf. A002808, A103278.

Extensions

a(1) prepended by and a(2) corrected by Jinyuan Wang, Aug 12 2022

a(7)-a(8) from David A. Corneth, Aug 12 2022

a(9)-a(18) from David A. Corneth, Aug 12 2022, copied from A103278