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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
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
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. *)
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Oct 14 2014
STATUS
approved