login
A248768
Greatest k such that k^5 divides n!
4
1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 12, 12, 12, 12, 24, 24, 24, 24, 24, 24, 24, 24, 144, 720, 720, 720, 1440, 1440, 1440, 1440, 2880, 8640, 8640, 60480, 60480, 60480, 120960, 120960, 120960, 120960, 120960, 120960, 241920, 3628800, 3628800, 3628800, 7257600
OFFSET
1,8
COMMENTS
Every term divides all its successors.
LINKS
EXAMPLE
a(8) = 2 because 2^5 divides 8! and if k > 2 then k^5 does not divide 8!.
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