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A355627
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a(n) is the number of tuples (t_1, ..., t_k) with a positive integer k and integers 2 <= t_1 <= ... <= t_k such that n = Product_{i = 1..k} (3 + 1/t_i).
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6
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2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50, 14, 0, 2, 9, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9291, 1668, 0, 2170, 226, 0, 1052, 59, 0
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OFFSET
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10,1
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COMMENTS
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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.
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LINKS
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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