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

%I A248779 #7 Oct 27 2014 19:55:30
%S A248779 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,
%T A248779 630,45,120,24,6,2,1,70,630,315,720,120,24,6,2,1,7,210,2520,5040,720,
%U A248779 120,24,6,2,1,77,2100,280,1260,5040,720,120,24,6,2,1,231
%N A248779 Rectangular array, by antidiagonals:  T(m,n) = greatest (m+1)-th-power-free divisor of n!.
%C A248779 Row 1:  A055204, greatest squarefree divisor of n!
%C A248779 Row 2:  A145642, greatest cubefree divisor of n!
%C A248779 Row 3:  A248766, greatest 4th-power-free divisor of n!
%C A248779 Rows 4 to 7:  A248769, A248772, A248775, A248778.
%C A248779 (The divisors are here called "greatest" rather than "largest" because the name refers to ">", called "greater than".)
%H A248779 Clark Kimberling, <a href="/A248779/b248779.txt">Antidiagonals n = 1..60, flattened</a>
%e A248779 Northwest corner:
%e A248779 1   2   6   6   30   5    35    70
%e A248779 1   2   6   3   15   90   630   630
%e A248779 1   2   6   24  120  45   315   2520
%e A248779 1   2   6   24  120  720  5040  1260
%t A248779 f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
%t A248779 u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
%t A248779 v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
%t A248779 p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}]
%t A248779 t = Table[n!/p[m, n], {m, 2, 16}, {n, 1, 16}]; TableForm[t]  (* A248779 array *)
%t A248779 f = Table[t[[n - k + 1, k]], {n, 12}, {k, n, 1, -1}] // Flatten (* A248779 seq. *)
%Y A248779 Cf. A055204, A145642, A248766, A248769, A248772, A248775, A248778, A000142.
%K A248779 nonn,tabl,easy
%O A248779 1,2
%A A248779 _Clark Kimberling_, Oct 14 2014