login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
Sequence in context: A360298 A033643 A050211 * A263713 A242427 A319545
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 14 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)