A355516 a(n) is the number of distinct integer values of Product_{k=1..n} (2 + 1/t_k) with integers t_k > 1.

1, 2, 5, 11, 29, 70, 164, 392, 933

Offset

2,2

Links

Table of n, a(n) for n=2..10.

Example

a(2) = 1: The only representable integer is 5 = (2 + 1/3) * (2 + 1/7).
a(3) = 2: 9 and 11 can be represented; 9 = (2 + 1/9) * (2 + 1/13) * (2 + 1/19) and 10 other ways; 11 = (2 + 1/3)*(2 + 1/5)*(2 + 1/7) = (2 + 1/3)^2 * (2 + 1/49).

Prog

(PARI) see link in A355626.

Crossrefs

A355626 provides more information.

A355628 same problem with factors (3 + 1/t_k).

Cf. A355243.

Sequence in context: A215939 A309857 A117719 * A359661 A316769 A192785

Adjacent sequences: A355513 A355514 A355515 * A355517 A355518 A355519

Keyword

nonn,hard,more

Author

Hugo Pfoertner and Markus Sigg, Jul 16 2022

Status

approved