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

2,4

Links

Table of n, a(n) for n=2..106.

Index entries for sequences related to factorial numbers.

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A011371, A054861, A011776.

Sequence in context: A226306 A124921 A090623 * A367824 A087283 A355924

Adjacent sequences: A098091 A098092 A098093 * A098095 A098096 A098097

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Sep 14 2004

Status

approved