A393396 Irregular triangle read by rows: the n-th row gives the list of d^(n/d) where d is a divisor of n.

1, 1, 2, 1, 3, 1, 4, 4, 1, 5, 1, 8, 9, 6, 1, 7, 1, 16, 16, 8, 1, 27, 9, 1, 32, 25, 10, 1, 11, 1, 64, 81, 64, 36, 12, 1, 13, 1, 128, 49, 14, 1, 243, 125, 15, 1, 256, 256, 64, 16, 1, 17, 1, 512, 729, 216, 81, 18, 1, 19, 1, 1024, 1024, 625, 100, 20, 1, 2187, 343, 21, 1, 2048, 121, 22

Offset

1,3

Links

Stefano Spezia, Table of n, a(n) for n = 1..9534 (first 1300 rows of the triangle)

Example

The irregular triangle begins as:
  1;
  1,  2;
  1,  3;
  1,  4, 4;
  1,  5;
  1,  8, 9, 6;
  1,  7;
  1, 16, 16, 8;
  1, 27, 9;
  1, 32, 25, 10;
  1, 11;
  1, 64, 81, 64, 36, 12;
  ...

Mathematica

row[n_]:=Table[d^(n/d), {d, Divisors[n]}]; Array[row, 22]//Flatten

Crossrefs

Cf. A000005 (row lengths), A000012 (1st column), A055225 (row sums), A027750, A275465 (2nd column), A393226, A393397.

Sequence in context: A278575 A386500 A393397 * A381003 A333879 A175126

Adjacent sequences: A393393 A393394 A393395 * A393397 A393398 A393399

Keyword

nonn,easy,look,tabf

Author

Stefano Spezia, Feb 13 2026

Status

approved