A387835 Irregular table read by rows: T(n,k) is the greatest number m such that m^k divides n, where k = 1..A051903(n).

2, 3, 4, 2, 5, 6, 7, 8, 2, 2, 9, 3, 10, 11, 12, 2, 13, 14, 15, 16, 4, 2, 2, 17, 18, 3, 19, 20, 2, 21, 22, 23, 24, 2, 2, 25, 5, 26, 27, 3, 3, 28, 2, 29, 30, 31, 32, 4, 2, 2, 2, 33, 34, 35, 36, 6, 37, 38, 39, 40, 2, 2, 41, 42, 43, 44, 2, 45, 3, 46, 47, 48, 4, 2, 2

Offset

2,1

Comments

The terms in a row are nonincreasing.

Links

Felix Huber, Rows n = 2..5872, flattened

Formula

a(n) >= 2.

T(n,1) = n.

T(n,k) >= T(n,k+1) for A051903(n) > 1 and k = 1..A051903(n)-1.

Example

The table T(n,k) begins:
   n\k  1   2   3   4   ...
   2:   2
   3:   3
   4:   4   2
   5:   5
   6:   6
   7:   7
   8:   8   2   2
   9:   9   3
  10:  10
  11:  11
  12:  12   2
  13:  13
  14:  14
  15:  15
  16:  16   4   2   2
  ...

Maple

T:=(n, k)->mul(i[1]^iquo(i[2], k), i in ifactors(n)[2]);
seq(seq(T(n, k), k=1..max(map2(op, 2, ifactors(n)[2]))), n=2..48);

Crossrefs

Cf. A001597, A034699, A051903, A052409, A203025.

Sequence in context: A368693 A333235 A295887 * A293450 A322990 A120636

Adjacent sequences: A387832 A387833 A387834 * A387836 A387837 A387838

Keyword

nonn,tabf,easy

Author

Felix Huber, Sep 23 2025

Status

approved