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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).
1
0, 1, 11, 430, 364693
OFFSET
1,3
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).
Sequence in context: A197770 A287065 A337527 * A140840 A175158 A360066
KEYWORD
nonn,hard,more
AUTHOR
Hugo Pfoertner and Markus Sigg, Aug 27 2022
STATUS
approved