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A335234 Number of partitions of k_n into two parts (s,t) such that k_n | s*t, where k_n is the n-th nonsquarefree number (A013929). 2
1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 3, 2, 1, 1, 1, 1, 1, 4, 1, 3, 2, 1, 2, 4, 1, 1, 1, 1, 2, 3, 1, 5, 1, 3, 2, 1, 1, 1, 5, 1, 2, 1, 4, 1, 1, 1, 1, 6, 3, 1, 2, 1, 1, 1, 2, 4, 1, 1, 6, 1, 1, 2, 2, 3, 1, 1, 1, 4, 7, 1, 5, 1, 1, 2, 1, 3, 1, 2, 7, 1, 1, 1, 1, 2, 5, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
a(n) >= 1.
LINKS
EXAMPLE
a(4) = 1; The 4th nonsquarefree number, A013929(4) = 12 has 6 partitions into two parts: (11,1), (10,2), (9,3), (8,4), (7,5) and (6,6) with corresponding products 11, 20, 27, 32, 35, 36. A013929(4) = 12 only divides the product 36, so a(4) = 1.
a(5) = 2; The 5th nonsquarefree number, A013929(5) = 16 has 8 partitions into two parts: (15,1), (14,2), (13,3), (12,4), (11,5), (10,6), (9,7) and (8,8) with corresponding products 15, 28, 39, 48, 55, 60, 63 and 64. A013929(5) = 16 divides two of these products, 48 and 64, so a(5) = 2.
MATHEMATICA
Table[If[Sum[(1 - Ceiling[(i*(n - i))/n] + Floor[(i*(n - i))/n]), {i, Floor[n/2]}] > 0, Sum[(1 - Ceiling[(i*(n - i))/n] + Floor[(i*(n - i))/n]), {i, Floor[n/2]}], {}], {n, 300}] // Flatten
CROSSREFS
Cf. A013929.
Sequence in context: A296772 A228525 A352823 * A353854 A217467 A268057
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 09 2020
STATUS
approved

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Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)