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A248769
Greatest 5th-power-free divisor of n!.
4
1, 2, 6, 24, 120, 720, 5040, 1260, 11340, 113400, 1247400, 1925, 25025, 350350, 5255250, 2627625, 44669625, 804053250, 15277011750, 305540235000, 6416344935000, 141159588570000, 3246670537110000, 10020588077500, 80164704620, 2084282320120, 56275622643240
OFFSET
1,2
LINKS
FORMULA
a(n) = n!/A248767(n).
EXAMPLE
a(8) = 1260 because 1260 divides 8! and if k > 1260 divides 8!, then h^5 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 = 5; Table[p[m, n], {n, 1, z}] (* A248767 *)
Table[p[m, n]^(1/m), {n, 1, z}] (* A248768 *)
Table[n!/p[m, n], {n, 1, z}] (* A248769 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 14 2014
STATUS
approved