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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

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

Cf. A248770, A248771, A000142.

Sequence in context: A090583 A248775 A108889 * A033645 A248769 A319547

Adjacent sequences:  A248769 A248770 A248771 * A248773 A248774 A248775

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 14 2014

STATUS

approved

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Last modified August 7 17:44 EDT 2020. Contains 336278 sequences. (Running on oeis4.)