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A248775 Greatest 7th-power-free divisor of n!. 4
1, 2, 6, 24, 120, 720, 5040, 315, 2835, 28350, 311850, 3742200, 48648600, 681080400, 10216206000, 1277025750, 21709437750, 178678500, 3394891500, 67897830000, 1425854430000, 31368797460000, 721482341580000, 135277939046250, 3381948476156250 (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!/A248773(n).

EXAMPLE

a(8) = 315 because 315 divides 8! and if k > 315 divides 8!, then h^7 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 = 7; Table[p[m, n], {n, 1, z}]  (* A248773 *)

Table[p[m, n]^(1/m), {n, 1, z}]   (* A248774 *)

Table[n!/p[m, n], {n, 1, z}]      (* A248775 *)

CROSSREFS

Cf. A248773, A248774, A000142.

Sequence in context: A052399 A177553 A090583 * A108889 A248772 A033645

Adjacent sequences:  A248772 A248773 A248774 * A248776 A248777 A248778

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 14 2014

STATUS

approved

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Last modified August 8 02:22 EDT 2020. Contains 336290 sequences. (Running on oeis4.)