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A248767
Greatest 5th power integer that divides n!.
3
1, 1, 1, 1, 1, 1, 1, 32, 32, 32, 32, 248832, 248832, 248832, 248832, 7962624, 7962624, 7962624, 7962624, 7962624, 7962624, 7962624, 7962624, 61917364224, 193491763200000, 193491763200000, 193491763200000, 6191736422400000, 6191736422400000, 6191736422400000
OFFSET
1,8
COMMENTS
Every term divides all its successors.
LINKS
FORMULA
a(n) = n!/A248769(n).
EXAMPLE
a(8) = 32 because 32 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