A335438 Number of partitions of k_n into two distinct parts (s,t) such that k_n | s*t, where k_n = A335437(n).

1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 3, 2, 2, 1, 4, 1, 1, 3, 1, 4, 2, 1, 1, 5, 2, 1, 3, 1, 5, 3, 2, 1, 1, 4, 6, 1, 2, 1, 2, 1, 3, 6, 1, 4, 1, 1, 2, 1, 7, 1, 1, 5, 4, 3, 2, 2, 7, 1, 1, 1, 2, 1, 5, 8, 3, 1, 4, 1, 1, 1, 3, 8, 2, 1, 1, 6, 1, 3, 2, 1, 1, 2, 9, 5, 1, 1, 2, 1, 3

Offset

1,4

Comments

a(n) >= 1.

Links

Table of n, a(n) for n=1..92.

Index entries for sequences related to partitions

Example

a(2) = 1; A335437(2) = 16 has exactly one partition into two distinct parts (12,4), such that 16 | 12*4 = 48. Therefore, a(2) = 1.

Mathematica

Table[If[Sum[(1 - Ceiling[(i*(n - i))/n] + Floor[(i*(n - i))/n]), {i, Floor[(n - 1)/2]}] > 0, Sum[(1 - Ceiling[(i*(n - i))/n] + Floor[(i*(n - i))/n]), {i, Floor[(n - 1)/2]}], {}], {n, 400}] // Flatten

Crossrefs

Cf. A013929, A335234, A335437.

Sequence in context: A228429 A108316 A322426 * A145574 A182579 A290737

Adjacent sequences: A335435 A335436 A335437 * A335439 A335440 A335441

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 10 2020

Status

approved