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A098094
T(n,k) = greatest e such that k^e divides n!, 2<=k<=n (triangle read by rows).
0
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
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
KEYWORD
nonn,tabl
AUTHOR
Reinhard Zumkeller, Sep 14 2004
STATUS
approved