A295908 Triangle in which n-th row lists divisors d of n such that n/d is squarefree.

1, 1, 2, 1, 3, 2, 4, 1, 5, 1, 2, 3, 6, 1, 7, 4, 8, 3, 9, 1, 2, 5, 10, 1, 11, 2, 4, 6, 12, 1, 13, 1, 2, 7, 14, 1, 3, 5, 15, 8, 16, 1, 17, 3, 6, 9, 18, 1, 19, 2, 4, 10, 20, 1, 3, 7, 21, 1, 2, 11, 22, 1, 23, 4, 8, 12, 24, 5, 25, 1, 2, 13, 26, 9, 27, 2, 4, 14, 28

Offset: 1

Author

Rémy Sigrist, Nov 29 2017

Keywords

• nonn
• tabf

Comments

For any n > 0:

- the n-th row has A034444(n) terms,

- the n-th row has sum A001615(n),

- the n-th row has leading term A003557(n).

Examples

			Triangle begins:
  1:  [1]
  2:  [1, 2]
  3:  [1, 3]
  4:  [2, 4]
  5:  [1, 5]
  6:  [1, 2, 3, 6]
  7:  [1, 7]
  8:  [4, 8]
  9:  [3, 9]
  10: [1, 2, 5, 10]
  11: [1, 11]
  12: [2, 4, 6, 12]
  13: [1, 13]
  14: [1, 2, 7, 14]
  15: [1, 3, 5, 15]
  16: [8, 16]
  17: [1, 17]
  18: [3, 6, 9, 18]
  19: [1, 19]
  20: [2, 4, 10, 20]
		

Crossrefs

Cf. A001615 (row sums), A003557, A005117, A034444 (row lengths), A206778.

Programs

PARI

for (n=1, 28, fordiv (n, d, if (issquarefree(n/d), print1 (d ", "))))

Formula

T(n, k) = n / A206778(n, A034444(n) - k + 1) for any n > 0 and k such that 1 <= k <= A034444(n).