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A248779 Rectangular array, by antidiagonals:  T(m,n) = greatest (m+1)-th-power-free divisor of n!. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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: A331654 A302690 A030304 * A286030 A208905 A208749

Adjacent sequences:  A248776 A248777 A248778 * A248780 A248781 A248782

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Oct 14 2014

STATUS

approved

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Last modified September 20 07:21 EDT 2020. Contains 337264 sequences. (Running on oeis4.)