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A355629 a(n) is the number of tuples (t_1, ..., t_n) with integers 2 <= t_1 <= ... <= t_n such that 3^n + 1 = Product_{i = 1..n} (3 + 1/t_i).

%I A355629 #17 Sep 18 2022 17:05:36
%S A355629 0,2,50,9291
%N A355629 a(n) is the number of tuples (t_1, ..., t_n) with integers 2 <= t_1 <= ... <= t_n such that 3^n + 1 = Product_{i = 1..n} (3 + 1/t_i).
%e A355629 a(2) = 2: 3^2 + 1 = 10 can be expressed as (3 + 1/4) * (3 + 1/13) and as (3 + 1/5) * (3 + 1/8);
%e A355629 a(3) = 50:  There are 50 representations of 3^3 + 1 = 28 with 10 <= min(t_i) <= 23 and 38 <= max(t_i) <= 8773. A product with minimal t_1 and maximal t_3 is 28 = (3 + 1/10) * (3 + 1/94) * (3 + 1/8773), maximal t_1 and minimal t_3 occur in 28 = (3 + 1/23) * (3 + 1/25) * (3 + 1/38).
%o A355629 (PARI) See A355626.
%Y A355629 Cf. A034472, A355626, A355627, A355628, A355630, A355631.
%Y A355629 A356210 is the same problem with target 2^n + 1 and factors (2 + 1/t_k).
%K A355629 bref,hard,more,nonn
%O A355629 1,2
%A A355629 _Markus Sigg_, Jul 15 2022