login
A248772
Greatest 6th-power-free divisor of n!.
4
1, 2, 6, 24, 120, 720, 5040, 630, 5670, 56700, 623700, 7484400, 97297200, 1362160800, 28028000, 7007000, 119119000, 2144142000, 40738698000, 12730843125, 267347705625, 5881649523750, 135277939046250, 3246670537110000, 5194672859376, 135061494343776
OFFSET
1,2
LINKS
FORMULA
a(n) = n!/A248770(n).
EXAMPLE
a(8) = 630 because 630 divides 8! and if k > 630 divides 8!, then h^6 divides 8!/k for some h > 1.
MATHEMATICA
z = 50; 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]]}];
m = 6; Table[p[m, n], {n, 1, z}] (* A248770 *)
Table[p[m, n]^(1/m), {n, 1, z}] (* A248771 *)
Table[n!/p[m, n], {n, 1, z}] (* A248772 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 14 2014
STATUS
approved