A248779 Rectangular array, by antidiagonals: T(m,n) = greatest (m+1)-th-power-free divisor of n!.

1, 2, 1, 6, 2, 1, 6, 6, 2, 1, 30, 3, 6, 2, 1, 5, 15, 24, 6, 2, 1, 35, 90, 120, 24, 6, 2, 1, 70, 630, 45, 120, 24, 6, 2, 1, 70, 630, 315, 720, 120, 24, 6, 2, 1, 7, 210, 2520, 5040, 720, 120, 24, 6, 2, 1, 77, 2100, 280, 1260, 5040, 720, 120, 24, 6, 2, 1, 231

Offset: 1

Author

Clark Kimberling, Oct 14 2014

Keywords

• nonn
• tabl
• easy

Comments

Row 1: A055204, greatest squarefree divisor of n!

Row 2: A145642, greatest cubefree divisor of n!

Row 3: A248766, greatest 4th-power-free divisor of n!

Rows 4 to 7: A248769, A248772, A248775, A248778.

(The divisors are here called "greatest" rather than "largest" because the name refers to ">", called "greater than".)

Examples

			Northwest corner:
1   2   6   6   30   5    35    70
1   2   6   3   15   90   630   630
1   2   6   24  120  45   315   2520
1   2   6   24  120  720  5040  1260
		

Links

• Clark Kimberling, Antidiagonals n = 1..60, flattened

Crossrefs

Cf. A055204, A145642, A248766, A248769, A248772, A248775, A248778, A000142.

Programs

Mathematica

f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}]
t = Table[n!/p[m, n], {m, 2, 16}, {n, 1, 16}]; TableForm[t]  (* A248779 array *)
f = Table[t[[n - k + 1, k]], {n, 12}, {k, n, 1, -1}] // Flatten (* A248779 seq. *)