A213919 Triangle read by rows: T(n,m) = (n/k)^(k-1), where k is the m-th divisor of n, 1 <= m <= tau(n).

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 4, 1, 1, 1, 1, 4, 8, 1, 1, 9, 1, 1, 5, 16, 1, 1, 1, 1, 6, 16, 27, 32, 1, 1, 1, 1, 7, 64, 1, 1, 25, 81, 1, 1, 8, 64, 128, 1, 1, 1, 1, 9, 36, 243, 256, 1, 1, 1, 1, 10, 125, 256, 512, 1, 1, 49, 729, 1, 1, 11, 1024, 1, 1, 1, 1, 12, 64, 216, 1024, 2187, 2048, 1, 1, 625, 1, 1, 13, 4096, 1, 1, 81, 6561, 1, 1, 14, 343, 4096

Offset: 1

Author

Gerasimov Sergey, Mar 05 2013

Keywords

• nonn
• tabf

Comments

Divisor k of composite number n with maximal value (n/k)^(k-1): 2, 3, 4, 3, 5, 6, 7, 5, 8, 9, 10, 7, 11, 8, 5, 13, 9, 14,...

Examples

			Triangle begins:
  1;
  1, 1;
  1, 1;
  1, 2, 1;
  1, 1;
  1, 3, 4, 1;
  1, 1;
  1, 4, 8, 1;
  1, 9, 1;
  1, 5, 16, 1;
  1, 1;
  1, 6, 16, 27, 32, 1.
		

Crossrefs

Cf. A000005 (row lengths), A027750, A087909 (row sums), A167401, A208239.

Formula

T(n,k) = A027750(n, A000005(n) + 1 - k)/(A027750(n,k) - 1), 1 <= k <= A000005(n).

Extensions

a(83) corrected by Jason Yuen, Oct 27 2024