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A248766 Greatest 4th-power-free divisor of n! 4
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 (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!/A248764(n).

EXAMPLE

a(6) = 45 because 45 divides 6! and if k > 45 divides 6!, then h^4 divides 6!/k for some h > 1.

MATHEMATICA

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 *)

CROSSREFS

Cf. A248764, A248765, A000142.

Sequence in context: A008336 A033643 A050211 * A263713 A242427 A319545

Adjacent sequences:  A248763 A248764 A248765 * A248767 A248768 A248769

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 14 2014

STATUS

approved

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Last modified November 20 14:28 EST 2018. Contains 317402 sequences. (Running on oeis4.)