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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.

%I A339469 #37 Aug 12 2022 12:37:20
%S A339469 8,72,1200,37800,83160,846720,1965600,15724800,34927200,279417600,
%T A339469 1437836400,11502691200,5751345600,160626866400,46010764800,
%U A339469 1927522396800,8561475468000,80173757664000
%N 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.
%C A339469 This sequence is defined for n 3-tuples. I have no result for n s-tuples, s >= 4.
%C A339469 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.
%C A339469 See A103278 if the requirement of parts >= 2 is dropped. - _R. J. Mathar_, Dec 11 2020
%e A339469 n = 1, k = 8, 8 = 2*2*2 and 2+2+2=6;
%e A339469 n = 2, k = 72, 72 = 6*6*2=8*3*3 and 6+6+2=8+3+3;
%e A339469 n = 3, k = 1200, 1200 = 20*15*4 = 24*10*5 = 25*8*6 and 20+15+4 = 24+10+5 = 25+8+6;
%e A339469 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.
%Y A339469 Cf. A002808, A103278.
%K A339469 nonn,more
%O A339469 1,1
%A A339469 _Ctibor O. Zizka_, Dec 06 2020
%E A339469 a(1) prepended by and a(2) corrected by _Jinyuan Wang_, Aug 12 2022
%E A339469 a(7)-a(8) from _David A. Corneth_, Aug 12 2022
%E A339469 a(9)-a(18) from _David A. Corneth_, Aug 12 2022, copied from A103278