A356210 a(n) is the number of tuples (t_1, ..., t_n) with integers 2 <= t_1 <= ... <= t_n such that 2^n + 1 = Product_{i = 1..n} (2 + 1/t_i).

0, 1, 11, 430, 364693

Offset

1,3

Links

Table of n, a(n) for n=1..5.

Example

a(1) = 0 trivially;
a(2) = 1 because the only way to express 2^2 + 1 = 5 is (2 + 1/3)*(2 + 1/7);
a(3) = 11: the lexicographically earliest tuple is (5, 23, 517), and the lexicographically latest tuple is (9, 13, 19);
a(4) = 430: lexicographically earliest is (9, 77, 5891, 34700935), lexicographically latest is (25, 27, 37, 55);
a(5) = 364693: lexicographically earliest is (17, 281, 78821, 6212710631, 38597773381434062845), lexicographically latest is (57, 77, 85, 93, 115).

Prog

(PARI) see link in A355626; set s=2 and use function a355629(n).

Crossrefs

A355626 provides more information.

A355629 is the same problem with target 3^n + 1 and factors (3 + 1/t_k).

Cf. A355243, A355516, A356211.

Sequence in context: A197770 A287065 A337527 * A140840 A175158 A360066

Adjacent sequences: A356207 A356208 A356209 * A356211 A356212 A356213

Keyword

nonn,hard,more

Author

Hugo Pfoertner and Markus Sigg, Aug 27 2022

Status

approved