A124832 Table of exponents of prime factorizations in A025487.

1, 2, 1, 1, 3, 2, 1, 4, 3, 1, 1, 1, 1, 5, 2, 2, 4, 1, 2, 1, 1, 6, 3, 2, 5, 1, 3, 1, 1, 7, 4, 2, 2, 2, 1, 6, 1, 1, 1, 1, 1, 3, 3, 4, 1, 1, 8, 5, 2, 3, 2, 1, 7, 1, 2, 1, 1, 1, 4, 3, 5, 1, 1, 9, 6, 2, 4, 2, 1, 8, 1, 3, 1, 1, 1, 5, 3, 2, 2, 2, 6, 1, 1, 10, 3, 3, 1, 7, 2, 2, 2, 1, 1, 4, 4, 5, 2, 1, 9, 1, 4, 1, 1, 1, 6

Offset

2,2

Comments

This is an enumeration of all partitions.

Links

Michael De Vlieger, Table of n, a(n) for n = 2..10820 (rows 2 <= n <= 2500, first 106 terms from Ray Chandler).

Formula

A025487(n) = Product_{k=1..A061394(n)} prime(k)^T(n,k). [Edited by M. F. Hasler, Oct 12 2018]

Example

From M. F. Hasler, Oct 12 2018: (Start)
The table starts as follows:
  n : signature   (A025487(n) = factorization)
  1 : []          (1 = empty product)
  2 : [1]         (2 = 2^1)
  3 : [2]         (4 = 2^2)
  4 : [1, 1]      (6 = 2^1 * 3^1)
  5 : [3]         (8 = 2^3)
  6 : [2, 1]      (12 = 2^2 * 3^1)
  7 : [4]         (16 = 2^4)
  8 : [3,1]       (24 = 2^3 * 3^1)
  9 : [1, 1, 1]   (30 = 2^1 * 3^1 * 5^1)
  etc. (End)

Mathematica

Map[FactorInteger[#][[All, -1]] &, Import["https://oeis.org/A025487/b025487.txt", "Data"][[2 ;; 48, -1]] ] // Flatten (* Michael De Vlieger, Feb 06 2020 *)

Prog

(PARI) A124832_row(n)=factor(A025487(n))[, 2] \\ M. F. Hasler, Oct 12 2018

Crossrefs

Cf. A025487, A036041 (row sums), A061394 (row lengths), A124829, A036036, A080577.

Sequence in context: A124829 A093394 A094363 * A226130 A137569 A266715

Adjacent sequences: A124829 A124830 A124831 * A124833 A124834 A124835

Keyword

nonn,tabf

Author

Franklin T. Adams-Watters, Nov 09 2006

Extensions

Erroneous explanations in cross-references corrected by M. F. Hasler, Oct 12 2018

Status

approved