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

1,2

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".)

Links

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

Example

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

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. *)

Crossrefs

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

Sequence in context: A346864 A302690 A030304 * A286030 A343684 A208905

Adjacent sequences: A248776 A248777 A248778 * A248780 A248781 A248782

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved