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).

0, 2, 50, 9291

Offset

1,2

Links

Table of n, a(n) for n=1..4.

Example

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);
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).

Prog

(PARI) See A355626.

Crossrefs

Cf. A034472, A355626, A355627, A355628, A355630, A355631.

A356210 is the same problem with target 2^n + 1 and factors (2 + 1/t_k).

Sequence in context: A274485 A210919 A210924 * A203766 A197487 A080293

Adjacent sequences: A355626 A355627 A355628 * A355630 A355631 A355632

Keyword

bref,hard,more,nonn

Author

Markus Sigg, Jul 15 2022

Status

approved