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A248766
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Greatest 4th-power-free divisor of n!
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4
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1, 2, 6, 24, 120, 45, 315, 2520, 280, 175, 1925, 23100, 300300, 4204200, 63063000, 63063000, 1072071000, 14889875, 282907625, 9053044, 190113924, 4182506328, 96197645544, 144296468316, 3607411707900, 93792704405400, 31264234801800, 22787343150, 660832951350
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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a(6) = 45 because 45 divides 6! and if k > 45 divides 6!, then h^4 divides 6!/k for some h > 1.
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MATHEMATICA
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z = 40; 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 = 4; Table[p[m, n], {n, 1, z}] (* A248764 *)
Table[p[m, n]^(1/m), {n, 1, z}] (* A248765 *)
Table[n!/p[m, n], {n, 1, z}] (* A248766 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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