OFFSET
10,1
COMMENTS
Because 3^k < Product_{i = 1..k} (3 + 1/t_i) < 3.5^k, a(n) > 0 is possible only for 10 <= n <= 12 (k = 2), 28 <= n <= 42 (k = 3), 82 <= n <= 150 (k = 4), 244 <= n <= 525 (k = 5) etc. For n <= 19683, there can exist at most one k such that n can be written as a product of k factors (3 + 1/t_i).
a(n) = 0 when n is a multiple of 3: Suppose n = Product_{i = 1..k) (3 + 1/t_i). Then n * Product_{i = 1..k} t_i = Product_{i = 1..k} (3 * t_i + 1). The right hand side is not a multiple of 3, so neither n nor any of the t_i can be a multiple of 3.
a(n) > 0 iff n is in A355631.
LINKS
Markus Sigg, Table of n, a(n) for n = 10..243
PROG
(PARI) See A355626.
CROSSREFS
KEYWORD
nonn
AUTHOR
Markus Sigg, Jul 15 2022
STATUS
approved