A098094 T(n,k) = greatest e such that k^e divides n!, 2<=k<=n (triangle read by rows).

1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 4, 2, 2, 1, 2, 4, 2, 2, 1, 2, 1, 7, 2, 3, 1, 2, 1, 2, 7, 4, 3, 1, 4, 1, 2, 2, 8, 4, 4, 2, 4, 1, 2, 2, 2, 8, 4, 4, 2, 4, 1, 2, 2, 2, 1, 10, 5, 5, 2, 5, 1, 3, 2, 2, 1, 5, 10, 5, 5, 2, 5, 1, 3, 2, 2, 1, 5, 1, 11, 5, 5, 2, 5, 2, 3, 2, 2, 1, 5, 1, 2, 11, 6, 5, 3, 6, 2, 3, 3, 3, 1, 5, 1, 2, 3

Offset: 2

Author

Reinhard Zumkeller, Sep 14 2004

Keywords

• nonn
• tabl

Examples

			Array begins:
  1
  1 1
  3 1 1
  3 1 1 1
  4 2 2 1 2
  ...
		

Links

• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A011371, A054861, A011776.

Programs

Mathematica

T[n_, k_] := IntegerExponent[n!, k];
Table[T[n, k], {n, 2, 15}, {k, 2, n}] // Flatten (* Jean-François Alcover, Sep 15 2021 *)

PARI

T(n,k) = valuation(n!, k); \\ Michel Marcus, Sep 15 2021

Formula

T(n,2) = A011371(n); T(n,3) = A054861(n) for n>2; T(n,n) = A011776(n).